Installing mods on any of the C&C titles is usually done best via a fan-made mod launcher.
For C&C Generals and C&C Generals Zero Hour, this mod launcher is called GenLauncher and it's fantastic.
It offers a single UI which allows you to install a variety of the most popular mods and easily toggle them on and off. You can also adjust a variety of settings, most importantly imo being the Camera Height. Vanilla is set to 0, but I play on 600 for a really zoomed out feel.
The mod launcher is completely free and has been virus checked by ModDB itself.
Please note, when modding any C&C game there is a very high chance your Anti-Virus will block something or delete a file as it will identify part of the installations as a virus, if something doesn't go right at any stage I would highly recommend temporarily disabling your anti-virus protection and then doing your install and then re-enabling.

The GenLauncher is downloaded from the site called ModDB which is a long-time player in the modding community. All mods are contained within this site and can be sorted by popularity, trending, release date etc...
GenLauncher comes will a easy-to-use UI which allows you to conveniently download the most popular mods. My personal favourites are: Shockwave, RedAlert, Generals 2

First we're going to install a Mod Launcher which comes with a bunch of config items.
Head over to GenLauncher's ModDB page and select 'files'.
Next, select the most recent version and it'll download.


Now, open your game's directory in SteamApps.
Open GenLauncher1006.zip and move the file 'GenLauncher.exe' to be within your game's root directory.
Then Run it and accept Windows Administrator permissions.
This window will now pop up.


Press 'ADD MOD!' and select from a list of the most popular mods. I'd recommend browsing ModDB's page by Most Popular to see which mod is right for you.
I've selected Generals 2, but feel free to try them all since they are very easy to swap in and out. Note that you can only have 1 mod active at a time.

You can also customise your settings

I would highly recommend sticking to this launcher to ensure everything runs smoothly.

First go to the properties of your Steam game.

Then enter in the path to your GenLauncher.exe followed by %command%.
The path must be enclosed within double quotation marks like shown in the image below.

1. Textures not loading
I have not personally had this issue, however, as Abang said in the comment's section, it's most likely caused by launching straight into mods without launching the base game at least once.
Please ensure you run C&C Generals ZH once before you start using GenLauncher, this is to ensure files are correctly initialised such as the mod folder in documents. This should fix texture issues.

2. Resolution support for anything other than 16:9
I have a 3440x1440 21:9 ultrawide monitor and I play the game in 1920x1080 in windowed mode to avoid all issue. When you play on a non 16:9 resolution, you will encounter stretching and inaccurate mouse selections.

3. My camera is too zoomed in
When in-game with GenLauncher, press 'Insert' or 'INS' on your keyboard to bring up the GenLauncher tools menu, from there adjust the Camera Height property to your liking, this can be change mid-match.

4. My game crashes when I launch into a skirmish
I had a lot of these, best thing to do is try a vanilla match and make sure you do NOT use the 'Random' options for AI. Some mods in the C&C franchise cause CTDs when the 'Random' option is used for AI such as the difficulty or faction. It's best to manually set these to prevent those issues.
Another fix could be to use the vanilla maps.