I warned you.
Have no fear, arachnophobes. I'll show no pictures.
First, the spider must be newly drowned. If more than a few minutes have elapsed, your only course of action is respectful disposal of the corpse. Unless your conscience calls for an act of contrition. I'll leave that up to you.
Get the spider out of the water. Bit obvious, yes, but must be said.
Depending on how long he's been in the water, he may be a little crumpled. If so, use a sturdy piece of paper or cardboard as a support. I recommend taking him outside for the rest. If you're successful in your efforts, you'll have a live spider on your paper awake and ready to explore the world. If you're not, you can put him on the compost bin and go about your business.
Using a small paintbrush, carefully "paint" the spider out of its crumpled position into something resembling a normal spider resting pose. Legs should be untangled and body as straight as possible. I cannot stress how important it is to be gentle at this point if you don't want bits of detached spider sticking to your paintbrush. The paintbrush serves the purpose of not only being more gentle than your big, clumsy finger but it also removes the water that soaked into the poor little spider's exoskeleton. The paper helps with this, too.
If you see signs of movement at this time, don't freak out. It may be life returning or it may be the spider's legs collapsing inward from lack of blood pressure (meaning it's really dead and you should go through his pockets and look for loose change).
Once the spider's body has been returned to a semblance of normalcy, leave him alone. Put the paper in a quiet, shaded spot where the wind won't blow it away but the air has a chance to circulate and continue the drying process. Check on him as often as your nerves can handle.
If you're successful, the spider will revive and leave. If you're not, have some ice cream and try to get over it. You did more than 99.9% of people would ever do for a spider.