Do not put the whole thing into water if you don't have a mask with stainless steel mesh. You will get rust.
I'm an exponent of the bucket dunk method. Find a large bucket, put your favorite laundry detergent in there, fill with water and stuff mask in. Churn it up and down for a few minutes, remove and replace with clean water and rechurn. Repeat until you are suds-free. Dry mask.
I've also used a dip method to clean just the bib, this works fairly well.
I sweat fairly heavily when fencing, but I've had pretty good luck with making sure that I put the mask out to air dry immediately on coming home. If the weather is nice I also make sure to leave it outside where the sun can shine into it, UV kills bacteria, as well as drying the thing quickly.
If you do search of the archives, you should find several threads on this topic. One guy swears by putting the mask in the dishwasher. I'm waiting for someone to announce they just shower with their mask on
