When you make a regular martini (ie, gin or vodka, & vermouth), when it is
poured, it is (or should be) crystal clear. When you make a dirty martini,
it's rather discolored (from the olive brine), hence the name "dirty". If
there's another reason for it's name, I'm not aware of it.
Experiment and decide what flavors compliment each other. It's kinda like
being a cook....it's all about flavors melding and the way it sits and/or
expands on your tongue and in your mouth. It's a lot of trial and error, but
have fun with it!
:-)