The Perfect Martini cannot be made on the fly. If you don't have your bottle of gin and martini glasses already in the freezer, you can put them there today for your martini tomorrow.
It is not necessary to buy the most expensive gin. I find that Gilbey's Gin gives you the most quality for the money. If you only have vodka on hand, you cannot make a martini. I believe the vodka drink is called a V&V (vodka and vermouth).
You may as well buy the most expensive French dry vermouth. Noilly Pratt and none other. One bottle will last you long enough. You must not keep the vermouth in the freezer. It will do better in the refrigerator.
Fill a container with ice. Add one half shot of vermouth. Add three shots of gin. Shake or stir with vigor. You should experiment with different ratios of gin to vermouth till you find the one you like best. The traditional ratio is 2-1. I find 6-1 most satisfactory.
Take a martini glass from the freezer. Add one olive or a twist of lemon peel. Pour your martini into your glass, straining out all ice. From here, you're quite on your own.
Pray remember the words of James Thurber:
"One [martini] is about right.
Two is too many.
Three isn't nearly enough."