Nothing at this point.
The worst thing you can do to a wet phone is charge it.
The next worst thing you can do is turn it on.
The third worst thing you can do is leave (or put) the battery in. (Even if it's a phone with a non-removable battery, breaking the back cover and cutting a battery wire [either one] is cheaper to fix than replacing the phone.)
At this point you probably need a new motherboard. Take it to a repair shop or bring it into Samsung (if you're in the US, most Best Buy stores have Samsung people in the cellphone area) and get a repair estimate.
Next time, remove the battery immediately. Then bathe the phone in rubbing alcohol in a non-metallic container. Swish it around for about 5 minutes to get all the dirt, minerals, etc., out of it. (Alcohol isn't water, it absorbs water, so it dries the phone.) After about 5 minutes of this, drain the phone and replace the alcohol (it's full of water and dirt now). Do it again, drain, replace and once more. Three baths.
Wipe the battery down.
Put everything into a sealed container (you can use something like a Tupperware container - I use a gallon jar) filled with uncooked rice. Pour in some rice, put the phone and battery in and cover it with a few inches of rice. Seal the container and wait a week. (If you have a few pounds of silica gel that's even better.)
If you get to it fast enough, and clean it well enough, you have a pretty good chance of having saved the phone.
