When you start the game, and the start-up menu appears, click "data files". Here you can turn on any mod you have installed. You can turn them off in the same way, but your existing savegames may not function properly.
You can play one game with some mods, and another game with other mods, it is that easy to switch them.
Only problems that I can think of are mutual incompatibility, eg. if two mods create something in the very same spot - that will crash the game. Such problems are usually mentioned in the readme.
Installation is very simple: you have only to put modname.esm file in your Data Files directory, and sometimes other files in their respective folders.
The game is too easy or too hard as it is, depending how you play it. Mods bring some freshness and make the game interesting again.
There are many sites with mods, for example:
http://thelys.free.fr/mods.htm
http://morrowindfiles.com
just do a google search for "morrowind mods"