It's funny that we call the martini by the name of the diminishing ingredient. When the martini debuted it was 3 parts sweet red vermouth to 1 part sweet old tom gin, with bitters mixed in. The mixture evened out for a long time, with equal parts gin and vermouth, and the gin changed to London Dry style and the vermouth to French dry style. Martini and Rossi have long been the makers of vermouth and it is from them that the martini gets its name, despite since the advent of the olive (replacing an earlier cherry), the dry 2 olive martini can barely be said to have any vermouth.
I personally use a vegetable spritzer (plastic pump bottles available at kitchen stores) to "mist" my glass with Martini and Rossi vermouth. I prefer the barest pump. Many of my friends prefer two.
I loathe making a martini "dirty". Adding olive juice doesn't do it for me: I like the barest skim of olive juice across the top that comes from the fresh green pimento stuffed olives that are dropped in after pouring the gin.