Big Mathis uses mods for the terrain and scenery seen in his videos. The vehicles he uses are built with mods, which aren't required to use them. And his vehicles use skins to change the appearance of blocks.
All of these mods, vehicles, and skins you can download from the Steam Workshop. Simply go to Besiege in your library, and click the workshop button. From there you can search for machines, mods, and skins. Once you have found what you want, click the [+] icon when hovering over it. You are now subscribed to whatever it is.

If you just want to crash planes then the only thing you should get is skins and workshop machines.

The specific mods Big Mathis uses are:
For his videos,

• Besiege Custom Scene Mod, to change terrain and scenery.
  
• Additive Loading, to spawn in more than one vehicle.
  
• ColorMod, to change the color of his rotors.
  
• More Sound, some other sound effects are added in when editing the videos.

For his machines,

• Block Scaling Tools, to change the size of blocks.
  
• NoBounds, to change values past their vanilla limit.

Skins for his machines:
CCCanyon's Aluminiums
And whatever Steam says are required items.
Skins must be enabled under the gear icon in order to be displayed.

Big Mathis' Workshop

By clicking the gear icon in-game, a menu opens, one of the options under it is Advanced Building, with AB you can,

• Change the amount blocks are translated and rotated.
  
• Mirror blocks on any axis.
  
• Allow blocks to intersect when building.
  
• Duplicate blocks to translate and rotate.

When the translation, rotation, and mirror tools are selected, turning red, three smaller icons will appear just under the numbers. These are,

• Global, when enabled translation, rotation, and mirroring and locked to global axis instead of locally to the block.
  
• Center, when enabled translation, rotation, and mirroring are based on the block's primary trigger, when disabled translation, rotation, and mirroring are based on the center of the block.
  
• Linked, when enabled translation, rotation, and mirroring with the arrows move multiple blocks so that their form is preserved, when disabled translation, rotation, and mirroring move multiple blocks independently from one another.

When the symmetry tool is selected, turning red, three smaller icons will appear. These are,

• Axis, when enabled all axis appear when symmetry is enabled, when disabled symmetry is still enabled but does not do anything.
  
• Cursor, when enabled symmetrical blocks are translated, rotated, and mirrored at the same time. When disabled, only the selected block is.
  
• Eraser, when enabled blocks are deleted symmetrically, when disabled only the selected block is deleted.

Better FPS can be achieved by

• Lowering timescale, top right in sim.
  
• Lowering graphics settings and resolutions.
  
• Disabling effects under the gear icon.

Because of Unity, Besiege's physics are limited to one core, Besiege is more CPU than GPU reliant.

You can download machines others have already built by going to Besiege's steam workshop, and pressing the [+] button.
To use workshop machines, open the load machine menu, and click the steam workshop icon, you can then choose which machine you want.
To use mods go to the mods menu near the top right on the title screen, and ensure they are [ON], they may be enabled by default.

Vanilla Besiege has variables which can be changed, the speed of a wheel, the weight of a ballast, etc... In vanilla, there is a limit to how high these values can go, but by subscribing to the NoBounds mod, you can set these values to whatever you want.
By setting values to overflow, 10^19 for propellers, -10^21 for water cannons, 10^33 for vacuums, drag is applied. Overflow vacuums apply drag to all non-static objects perpendicular to them.

Blocks in Besiege have hidden scale values in X, Y, Z. Which are set to 1 by default. With the help of the Block Scaling Tools mod, you can edit these values freely. Block Scaling Tools also lets you copy and paste position, rotation, and scale. And scale multiple blocks together. A complete summary of information is available on the mod's page.

Being able to see colliders and connections is a must for small scale and complicated builds. With the Colliderscope mod, you can toggle on/off the view of various colliders and triggers.

Skins for blocks can be downloaded off of Besiege's steam workshop, they can change the look of a block, but not it's hitboxes.
Subscribing:
Find the skins you would like and press the [+] button to subscribe to them. Many skin themes are put into collections by the skin creator, by clicking their name > workshop items > collections, you can look at those themes, and subscribe to all of them with a single click by pressing [Subscribe to all].
Applying, Viewing, Options
In game under the gear icon, you must enable [Skins] under Visuals, in order to see and use skins. With it enabled, you can use the wrench tool on already placed blocks to change their skins.
If you want skins to be applied to blocks as you place them, select a block you would like to place, and click it once more. This will bring up a menu of different skins. To the right side of it are options to refresh, download more, and manage skins.

On the title screen, go to Multiverse and Level Editor.
If you are joining a game:
You can set a name and directly connect to an IP and port. The client must have the same mods as the host in order to join the game, if they are not the same a menu will pop up on the left, clicking on the buttons will fix any incompatibilities. If any of the buttons turn yellow, you have to restart your game in order to unload the mod(s).
If you are hosting:
You can set a name, set an optional password, and set a port.
Steam friends can join you by clicking your steam profile and pressing Join Game. If this isn't an option, you can give players your IP to directly connect to you. Your IP can be found in Server Management menu in the top right, to the left of the gear icon.
In the Server Management menu you can change server settings and replace Level Editor with a Playlist of levels.
In the Level Editor menu, in the gear icon, you can set player, block, and machine limits. Change scenes between, None, Barren, Tolbrynd, Mountain Top, Desert. Change Music, Game Rules, and other miscellaneous settings.

The boundary that surrounds the world hinders planes and other vehicles, to disable it you can subscribe to AddCustomModuleMod or Object Explorer, and select the no boundary option, or delete the walls respectively. AddCustomModuleMod is the simpler of the two and recommended for those starting out.

While Besiege offers preset resolutions and ratios, not everyone has said presets. By going into,
steam > steamapps > common > Besiege > Besiege_Data > config.xml,
you can type your resolution into <ScreenWidth> and <ScreenHeight>.

There are some bugs in Besiege that can be quite frustrating.

Symmetrical Vibration Glitch - After an update of the version of Unity used for Besiege, depending on the way certain blocks are placed and their weight, it will create a self amplifying motion. This often occurs when flexible blocks are created in a cross shape, or many low mass blocks are attached to a single low mass block. Increasing mass, or reinforcement can eliminate the problem.

Error : Limit Exceeds - When uploading an workshop item an error can occur on your screen saying "Error : Limit Exceeds". This issue has been widespread for games that use the steam workshop. There are many reasons why it might occur. The most likely problem is that your thumbnail is over 1000 kilobytes. Although it could be a numerous other reasons that do not have anything to do with your thumbnail. Also covered under, Can't Upload to Workshop.

Rocket Thrust - This won't happen if you do not use mods or modify your game files. When setting rocket thrust to 0x, the game will crash.

Phantom Torque - Where torque is exhibited on a part or assembly when it shouldn't be. The reasons for phantom torque are usually a result of force somewhere on the assembly or parts connecting to it. Weight, bending blocks, blocks colliding with other blocks, blocks connecting in an order that makes them do the previous, etc... See, Why your Symmetrical Build isn't acting like it.

1. To upload to workshop you must first save your machine.
2. Go into the load machines menu, and find your machine.
3. Click the steam icon on the bottom left of your machine.
4. Apply tags, upload or update.
5. Wait for steam to upload.
6. Write and edit.
7. Change privacy/publish.

You can change the thumbnail of creations by going to,
steam > steamapps > common > Besiege > Besiege_Data > SavedMachines >Thumbnails.
Make sure to replace the old thumbnail, and use the same name.
If you save in-game your newly changed thumbnail will be overwritten.
By doing this and uploading/updating your machine to workshop, you can change the thumbnail on workshop as well.

If you get an error that prevents you from uploading to the steam workshop you may need to try again. Since that obviously didn't work you've come here. These are a list of reasons why you may not be able to upload to the Workshop. There may be more not covered here.

• Steam is getting the incorrect information about the upload and denying it. Sign out and sign back into your steam client.
  
• Steam servers aren't working for whatever reason.
  
• Thumbnail is over 1MB, recommended size is 512x512 but any works as long as its under 1MB.
  
• Your Steam Cloud is full, turn on cloud saving, save a creation to cloud, turn off cloud saving, restart. You may need to properly delete the saves in your Steam Cloud, there are many guides online for that. To check if your Steam Cloud for a game is full go to library > right click the game and click properties > general.
  Alternatively, if the previous fix is not working, go in game, save folder, and disable cloud savings on your machines individually, disable cloud saving on machines individually by clicking on the cloud.
  
• If Steam Guard is being used, you may need to log out, log back in, and input your Steam Guard code.
  
• You may have empty saves in your Workshop, delete if you find any.
  
• Your Steam client may have a bug, reinstalling can fix it. A easier solution may be to install another steam just to upload.

It is possible to upload through SteamCMD. Following instructions from this guide should work, just change appid to 346010 and the corresponding files to Besiege files.

Sometimes when you build something symmetrically it really isn't symmetrical. But due to how Besiege prioritizes connections, even symmetrical builds can act unsymmetrical.

Build Direction: Triggers, which are how blocks connect to other blocks, prioritize connections to colliders, what they can attach to; to the rightmost collider. And if there are two colliders of the same distance, it's decided by block order. Build direction can completely mess up one side of your vehicle. To fix it, enable advanced building, press ctrl+a to select everything, and rotate your vehicle 90 degrees.
Proper build direction is 90 degrees from the starting orientation of your camera in barren expanse. Or parallel to the direction of the red arrow when the translate tool is selected on a fresh source cube.

Block Order: Is another way connections are prioritized. Blocks sit on a list of connection priority. The most recently placed block sits lowest on the list, and pushes up any older ones. A way to get lowest block priority is to delete and undo a part with ctrl+z. Can be partially visualized with cluster view.

Add Point Triggers: Smooth surface blocks and ballasts prioritize connections to add point triggers on large wheels and wing panels.

Prioritization is also decided by distance, angle, scale.

Overlapping Triggers: Primary triggers usually disable secondary triggers when intersecting. Mechanical triggers usually disable primary triggers when intersecting. Colliderscope displays triggers.

The most likely explanation is that Besiege has permissions to read but not write files. To fix this, turn on Take Ownership.

To most players clusters will never be something they need to know.
In the gear icon menu, under visuals, is [Cluster]. Clusters simplify calculations by grouping blocks together based on how they will move.
Two logs form one cluster, a log with a wheel on it forms two different clusters, a wheel with a log on it forms one cluster.
Clusters can be a single block, to as many blocks as you have.
When a cluster breaks, the broken parts turn into two different clusters.
Sometimes clusters turn grey, this usually happens because they have broken.
You can separate some blocks from clusters, for example a cannon, by deleting the block they were placed on and replacing it.
Clusters can affect physics, and the fewer you have the less laggy your creation will be.

The inputs given by controllers are supported by the base game and unity, and can be found in the unity documentation in Resources. The Joystick Mod, allows for ease of use, lerp, sensitivity, and the rest of what you would expect from controller controls.

By using the More Options mod you can change game control keys and even format machines to be controlled with the mouse.

These resources are made by others to provide information that's useful for building.
Besiege Wiki[besiege.fandom.com]
Besiege_Block_Status by Tamakoro[docs.google.com]
Besiege Bots Block Information (New)[docs.google.com]
CCCanyon's Blog[cccanyonbesiege.blogspot.com]
List of Potential Keybinds[docs.unity3d.com]