First, I assume you are not playing on a Mac. If so, visit the Civ V - Mac forum -- there is a sticky thread with instructions on how to deal with Mods on a Mac.
For Windows, fire up Steam, go to Library, and navigate to Civ V -- that page should have (among other things) a prominent section for the Civ V Steam Workshop. Select browse the workshop and rummage around. When you find mods you like, click the Subscribe button. Steam will automatically download the mods to the correct folder (although there are download glitches from time to time, so it may take a while for mods to show up).
If you are already in game, go to the main menu and click Mods. After the warning screen you will see what will probably be an empty screen (since you have no mods yet). Click browse at the bottom of the screen and it will take you to the Civ V Steam Workshop. Browse and subscribe from there.