Is copying game folders literally just ctrl-c and ctrl-v in Explorer, or is it done inside the Steam client? What about saved games?
It's all over the place, steam isn't exactly a software platform to run the games off of, it is mainly a distribution platform, so all games decide themselves where to place save files, sometimes its "my documents", sometimes somewhere in appdata, sometimes in the steam folder somewhere, or just somewhere under the game folder.
Copying games is almost copy paste. It' something like this:
1. Add another library location in the steam client (in settings)
2. Copy the game folder for the game you want to move (steam\steamapps\common\gamename) to the new location you created in step 1
3. Rightclick the game in steam and select "delete local content"
4. Reinstall the game, but instead select the new library location, steam will just verify the local files instead of redownloading them
(I personally just use a ssd and remove games im "done" with, makes for faster loading and whatnot, and my internet connection is fast enough anyways should i want to reinstall something)