The first step in identifying which of the workshop items that are asteroids, is the "asteroid" tag that authors are required to add to their workshop submission.

To give you a quick start, here is a link to all 'Asteroid' tagged Workshop items.

There are many asteroids in the workshop to choose from.
Find ones that you like and appeal to you, and simply subscribe to them.

Some asteroids may also require a second mod, which is a "voxel material". This defines additional materials that may be inside of the asteroid.
Be sure to subscribe to those additional mods if recommended by the asteroid author.

1. To load a subscribed asteroid into you game, first start Space Engineers.

2. Only worlds that are currently in "Creative" mode allow you to add asteroids in game. You can change a world from "Survival" to "Creative" temporarily to allow you to add asteroids, and then change it back later.

3. Select your world, and "Edit Settings".
Make sure you game is set to "Creative" mode.
One further suggestion is to "Enable Spectator" mode.

4. Select the "Mods" button.
In this window on the left hand side, you will see all currently subscribed mods that may be added in game.
You can filter specifically for asteroid with the Asteroid button at the top.

5. Select and add the asteroids you wish to add into your game.
But sure to add the additional "Voxel Material" mods that may be required.
Once you are done, press "OK" to return to the world selection menu.

6. Load your game.

7. Open the spawn menu with the "Shift+F10" keys.
From this menu you can spawn asteroids as well as components and tools.

8. Choose the desired asteroid from the drop down menu.
The name of a subscribed Asteroid mod may not necessarily match the list of names within the drop down list. Be sure to check any details within the subscribed mod that help you identify the name of the asteroid.
Now press "Spawn Asteroid".
A well authored asteroid should only take at most a few seconds to appear.

9. Place the asteroid where you require it.
You will be restricted in where you can place the new asteroid, as you "Cannot place asteroid over ships or players."

10. Use "Spectator" mode to place asteroids by pressing "F8".
By using Spectator mode, you will have more freedom to move about and place asteroids without been blocked by your player character.
Once finished, remember to press "F6" to return to your player.

11. Deleting asteroids.
If you have made a mistake in asteroid placement, place your cross hairs over the asteroid and press "Ctrl+X".
Make sure to read the dialog to confirm which asteroid you are deleting, this will prevent you from deleting the wrong asteroid.

12. Once you have placed the asteroid where you want it, do not forget to save!

There is a known issue with the game when you spawn a new asteroid that sometimes the collision mesh does not line up.
You simply have to save and reload the game to fix it.