First, take the computer apart and clean the board(s) with a ultrasonic cleaner or rubbing alcohol. If you have an ultrasonic cleaner and know how to use it, then that's the way to do it. The toothbrush works, sort of. In order to open the Mac, you'll need the Pentalobe screwdriver. You can find these in the iFixit 54 bit driver kit, or online. Just be aware buying the ones on eBay and Amazon that they're probably junk. I'd get the 54 bit driver kit and use that.
Once you open this machine up, clean the boards up to start. Once you do this, let them sit under a window for several hours. If you can wait 24 hours, then do so. Replace the battery too. Many times this will suffer too, and it fails in short order. Change it while you're in the computer.
You can probably leave the other parts untouched. It might be a good idea to clean the cables though. Here's the guides on how to take the computer apart. I'd also read the Electronics water damage Wiki, too.