The download a mod. Not any form of download will work; instead you have to start Civ V, go to the mods section. Then from there find a mod to download and select download.
(You don't get the achievement for going to Civfanatics mod folder)
Rate a mod: From the same location, click the "like" button.
Play a mod: After installing the mod, from the mods section "activate" it to select it and start a game with it; you'll have that achievement when it finishes creating the world. (You don't even need to hit end turn)