As said no real special daily or even monthly cleaning needed, use it then rinse well before hanging or standing to dry. I try to not use the same brush two days in a row as some of them take more than a day to dry.
When they seem to not hold as much water or I see soap gathering at the base of the bristles (when dry) I use a Borax solution to clean it but only because I already had some, shampoo or fairy liquid will do the job just as well. After cleaning I use white vinegar solution as a rinse and you can add glycerin if you feel you want the hair softer, which is the same as using the hair conditioner.