Most of the old wives' tales about saving wet phones just don't work. The bag of rice, a sunny window sill, a hair dryer, and the horrid oven method will quickly get you (and your phone) nowhere.
Having suffered through several waterlogged phones and sacrificial experiments, I've found only one unexpected method to be reliable.
If you're lucky enough to be reading this before any mishap, be sure to stock up on the supplies so that you're ready when your phone takes a dive.
Step 1. Without wasting time, turn off your phone. Do this within seconds of the accident -- even before you dry it off with your t-shirt. The goal is to cut the power before any water has a chance to hit the circuitry and short circuit it.
Step 2. Dry the outside of the phone with a lint-free towel, paying close attention to any ports, speakers, and microphones. Disassemble any parts -- like the SIM card and battery -- and dry them, too.
Step 3. Place the device and parts in a zip-top storage bag, along with a handful of silica gel packets. These are desiccants often found in new products (like shoes and bags), along with some grocery items (like beef jerky). They're designed to be very efficient at absorbing moisture.
Collect them as you find them for emergencies like these. Or, you can order silica gel packets online.
Step 4. Wait 72 hours. This is probably the hardest part, but rest assured that you'll be OK, even if you haven't checked Instagram in three days.
Step 5. Power your phone on. Three days have passed, giving the desiccants ample time to absorb the moisture. If you did everything right, your phone should be back in business.
A few important notes
Here's the deal: Much of this method relies on chance and a little luck. The most important part is that you rescued your phone quickly, and that it was powered off before any liquid hit the circuit boards.
Know that even if you were able to revive your phone, there's a chance that any water contact (or worse, chemical- or salt-laden water contact) will corrode the parts over time. So if a year later, your phone begins to die a slow and painful death, you'll know why.
Finally, your warranty is void. All phones have a water indicator that tells the manufacturer it went for a swim. The iPhone 5S's water indicator, for example, can be found inside the SIM card slot. When it gets wet, it changes color from white to red.