I work in the instrument shop of an oceanographic research lab, so as you can imagine, I get a LOT of water-damaged electronics dropped on my bench.
I always tell the boat crews that the most important thing is not to let the equipment dry out until it gets back to the shop. Assuming it was submerged in salt water or dirty water, the first thing to do ASAP (preferably still out in the field) is to disconnect power (pull the batteries out), rinse everything off as well as possible, then put the unit into a cooler or similar container filled with clean, fresh water. If the unit dries out with salt residue still coating things, the ensuing corrosion greatly complicates repair efforts.
Once a unit gets onto the bench, I unplug all the separable connectors, remove any socketed ICs or other similar components, and give everything another rinse with warm water (the tiny amount of detergent mentioned above is a good idea). Then a rinse with isopropyl alcohol, followed by a final rinse with distilled water. and a blow-dry with compressed air.
At this point, I will give everything a quick lookover for any obvious corrosion, and remove any soldered-in lithium backup batteries or other components that may not tolerate the next step--a proper drying at ~150F in a vacuum chamber for 24 hours.
After drying, another inspection for obvious damage, and reassembly. Mechanical parts need a complete relubrication, and I generally give all the connectors a shot of Deoxit or similar contact cleaner. Most equipment that was rescued quickly will operate properly at this point and can be returned to service.
Otherwise, standard troubleshooting techniques apply from here on out, with special attention for stuff like corroded PCB traces in hidden areas, open plated-through holes or vias, etc.