Stripping it all down and soaking it in plenty of alcohol is the best method, alcohol both keeps the residues dissolved and binds with the remaining water, wich will prevent it from getting caught under components and in other narrow places.

And most components on the circuitboard is alcoholresistant, since it is standard to wash circuitboards in alcohol directly after machinesoldering.
The most common alcohol used for cleaning is isopropanol or "technical alcohol" as it also is called, but denaturated ethanol would be okay too if that is the only thing that is close by.

Q-tip or toothbrushes is more something i would use when it already has dried once, but i dont really believe a cellphone is possible to save after the water has dried once, since it is so small components and circuittraces on it.