Luckily, the martini takes all comers (except for those who want to append some other word before -tini). All you need to jump into the fray is a solid understanding of your options; let The Spirit breakdown of martini basics guide the way.
Vodka or Gin
Historically, ordering a martini without clarifying your choice of spirit means you're going to get gin. If you perfer a vodka martini, go ahead and order it that way -- and consider skipping the vermouth altogether.
Shaken or Stirred
The primary issue here is dilution; shaking breaks more ice, introducing more water into the cocktail. Once you've settled on your preferred proportions of spirit and vermouth, we say diverge from the James Bond method and break out the bar spoon. (If you simply must shake, use good, well-frozen cracked ice that's not on the verge of melting).
Perfect, Dry, or Dirty
A perfect martini, like a perfect Manhattan or Rob Roy, simply means equal parts sweet and dry vermouth. Ordering your drink dry means you'd like only a little vermouth in the mix, while bone dry will get you no vermouth at all. A dirty martini includes a dash of olive brine.
If you don't want your martini naked, you can take it with a twist (a curl of lemon peel), or with an olive or two on a skewer. You can also opt for cocktail onions, a decision that turns your martini into a Gibson.