No one knows for definite when the martini was invented or who by but most cocktail historians (they exist, seriously) pin the late 1800s as the time period that a mixture of vermouth, gin and orange bitters became widely known as a martini (a cut-down of the name "Martinez Special").
Despite often finding it sitting behind a warm bar, vermouth is in fact a wine (fortified and aromatized) and should be kept cold in the fridge or you risk it going bad. Gin, for this cocktail, benefits from being kept in the freezer to help maintain a cold temperature. Gin itself always tastes better cold.
The orange bitters, often ignored, are an important part of making a great martini, helping to bring together the gin and vermouth, highlighting the scents and flavours that overlap.
1.5 oz Gin (London Dry preferably)
1.5 oz Dry Vermouth
3 dashes Orange Bitters
Combine all ingredients in a glass with ice. Stir until very cold and strain into a chilled cocktail glass or 'martini glass'. Garnish with a lemon peel twist or single olive on cocktail stick (do NOT add any of the juice from the olive jar aka a 'dirty martini'. Why would you want that horrible mix of preservation chemicals in your cocktail?)
A note on vodka martini
A vodka martini contains vodka instead of gin and has almost surpassed the classic martini in popularity. Thanks to smart and aggressive marketing in 50s and 60s America (most noticeable being the James Bond films' product placement) vodka went from being a drink only Eastern European immigrants had any interest in, to America’s best selling spirit. Why should you choose the classic of the vodka? Firstly, the vodka martini rose to popularity because of smart marketing not taste and secondly vodka is odourless, tasteless and colourless. It adds NOTHING to a cocktail other than alcohol.