The recipe of vodka martini is following: Put 5 or 6 ice cubes in a shaker.  Add the salt, then the lemon peel, then the vodka and vermouth.  Shake until the shaker frosts.  Place your choice of garnish in a martini glass and pour the vodka mixture over the garnish.  If you want ice in your martini, let the ice cubes float into the glass.  I like to leave the ice in my drink.  It makes for a "longer" drink and in the extra few minutes it takes to drain the glass...life takes on a clearer, more sane, focus.
It's worth saying few words about two main ingredients of vodka martini cocktail - vodka and martini.
Vodka is a drink which originated in Eastern Europe, the name stemming from the Russian word 'voda' meaning water or, as the Poles would say 'woda'. The first documented production of vodka in Russia was at the end of the 9th century, but the first known distillery at, Khylnovsk, was about two hundred years later as reported in the Vyatka Chronicle of 1174. Poland lays claim to having distilled vodka even earlier in the 8th century, but as this was a distillation of wine it might be more appropriate to consider it a crude brandy. The first identifiable Polish vodkas appeared in the 11th century when they were called 'gorzalka', originally used as medicines.
In these ancient times Russia produced several kinds of 'vodka' or 'hot wine' as it was then called. There was 'plain wine' (standard), 'good wine' (improved) and 'boyar wine' (high quality). In addition stronger types existed, distilled two ('double wine') or more times.
Vodka is made from grains, and traditionally from potatoes, this clear spirit origianted in eastern Europe. With the resurgence of the Martini and Cocktail Culture, Vodka is more popular than ever. Yes, we are not forgetting the classic gin martini, but the majority seem to prefer vodka, sorry.
Today vodka is distilled all over the worls in dozens of flavors from cherry to chocolate. Drinkers have taken to vodka for it's mixability and smooth nuetral taste.
Since early production methods were crude, vodka often contained impurities, so to mask these the distillers flavoured their spirits with fruit, herbs or spices.
Martini is called to be the perfect candidate for relaxation because it is a short drink.  If you had lots of time to sit and have a drink, you would use the time differently and you would most likely book a message.
A good Martini is a concoction of such perfect proportions that you are consumed by its ultimate reality. A slow sip sends you into a nirvana of slippery, viscous, chilling, specialness. At times it is reminiscent of the best summer you ever had as a child, and on other occassions it validates your adulthood like nothing else can. The origins of the Martini will probably never be agreed upon. Some say it was born in San Francisco mid-19th century, while others credit it to a New York Bartender named Martini who claimed he mixed the first in 1912. Some assume that it gets its name from the famous dry vermouth so commonly used in the drink, Martini & Rossi, or to the British made Martini & Henry rifle, while many like to believe it is named after a drink developed in Martinez, CA and originally called the Martini.
There are couple of the popular vodka martini recipes. The first one is called Detroit Martini.  Into a shaker half filled with ice, add a large (50ml) shot of vodka, a dash of sugar syrup, a dash of orange bitters and a sprig of mint. Shake very thoroughly for 20-30 seconds, and strain into a chilled martini glass. Garnish with another sprig of mint.
And the other is Blue Sky Martini - vodka martini with vermouth and a splash of blue curacao, which looks cool in a martini glass.
However the main view is one might like a drink made with Vodka, but it's not a Martini.