In this case the art is  CC-BY 3.0 and according to the description you need to credit him and this website.

So it would look something like this:

RPG Character Sprites Set By: Antifarea (http://antifarea.deviantart.com/) & OpenGameArt (http://opengameart.org/)

If there where no special directions you would just do:

RPG Character Sprites Set By: Antifarea (http://antifarea.deviantart.com/)

"I know everything here is free to use as long as we give credit to the site and artist."

This is not quite true. Rather (roughly):

"Everything is free to use (CC0) as long as you give credit appropriately (CC-BY), provided you publish any changes you make to the art (CC-BY-SA), and provided your game is GPLed (GPL)."

In case something has multiple licenses listed you get to choose which one to comply to.

Nah. Putting your game under the GPL basically means you have to make the source code available to everyone, alllow them to make modifications and release their own version (modified or not) of the software under the same terms (you can in turn take their code, modify and re-release).

GPL is the most restrictive license on OGA - not only does your program have to be free software, you can not even use a more permissive free and open source license for your game.

If you do not want others to be able to use your code, stay away from GPL-only artwork. The spritesheet you linked however is CC-BY - you are free to modify the artwork and use whatever license you want for your code, as long as you give credit. See verbalshadow's post.

Yeah, if you want to keep it simple, stick to CC-By licensed assets.  All you'll need to do is be sure to give credit in your game and you'll be fine.