A dry martini has very little vermouth (perhaps just a few drops), while a wet martini has a larger portion of vermouth (approx 3 to 1 gin to vermouth).
Contrary to what James Bond told you, there is no reason to shake a martini. Simply stir it with ice in a mixing glass, and strain into a chilled martini glass. Serve with a green olive.
See also: List of cocktails