Day job method:

I usually give everything a good soak in good flux remover (eg, MG Chemicals 413B) using a brush or Q-tip to get any burnt or big 'goobers' of flux loose. Then dab off as much of the flux remover as possible using a paper towel, and give a second soak in flux remover.

Then finish with a wash in deionized water, finally blow the water off with compressed air.