First off I don't really support the idea of duel types, but I've read people say it would be crazy over powered or confusing. The way I thought about it is like this, just using Muddy water as an example.
Cut the damage in half so 45.5 damage is water and 45.5 damage is ground. Not too complicated but it would probably suck if only the water or ground half gets the STAB, but that's just how I've thought of it.
I don't mind the idea of a move sharing another type. (IE: A move can be either Fire type or Electric but the STAB only works for the type it is at the current moment: IE:
Explosion: Normal or Fire Type : Same BP, however if it's fire type Fire Pokemon get obvious stab, and if normal, same thing (Normal Stab) however resistances match up as well.) --- Only insecure and ignorant people try to debase someone online based on their username.