Tools
This should without being said, but always use clean tools! Using dirty tools or ones previously used to make a drink can retain the flavor of the previously made drink.

Chilling
Chill your martini glass! Using a chilled martini glass will help keep your martini colder longer. To properly chill a glass, freeze it, or use a nifty little bartenders trick! Take the martini glass, fill it with ice and water. Filling the glass with water will increase the surface area that gets cold, instead of just having parts of the ice touch parts of the glass.

Shaking
Shake to your hearts content! Just remember, the more you shake your martini, the more it gets diluted and the cloudier it can get, but it gets colder this way. The less you shake, the more flavors you will retain, but it won’t be as cold.

On a side note, a classic martini is made with gin. It has been a recent trend to use regular and flavored vodkas for martinis.

Dry Martini – Traditionally uses more dry vermouth, however recent trends define a Dry Martini as using little or no vermouth.

Gibson – Garnish with a cocktail onion.

Perfect Martini – Use equal parts of sweet and dry vermouth.

Dirty Martini – Add a small amount of olive brine.

50-50 -Use equal parts of gin and dry vermouth.

Vodka Martini – Replace gin with vodka for a nice alternative.