Quick and easy; serves one.
Juice a fresh lemon.
Add 3-4 teaspoons (or to taste) of sugar. Stir until the sugar has dissolved. If you have time, place the mixture in the freezer for 20 minutes, or the fridge for an hour.
Into a martini glass pour a dash of vermouth, then equal measures of chilled vodka/gin and the lemon mixture.
Stir then serve with a strip of lemon peel as a garnish.
There are other variations which include triple sec, or you could rim the glass with sugar (as I did in the first picture), but otherwise, this is the fastest, easiest recipe I know. If you feel more adventurous try the Lemon Drop Martini with Foam or my own creation the Lemon and Lime Drop Martini.