Instead of going into the "Assets" file go into the "Mods" file, Here you will see the pre-made mods such as American Revolution and the Tutorial. Create a new folder (i.e. "Crayton's Mod") and then copy your "Assets" folder into here. Just look within the pre-existing mods to check if you've done it correctly.
You won't need to put/keep every file into your new mod folder, only those files which you have altered. To play, you can either go to the "Load Mod" button within the game or alter the "_Civ4Config" file. About 40% down the file there is a place to set your new mod as default (i.e. Mod = Mods\Crayton's Mod).