Choose a type of liquor that you want to use in your cocktail. It wouldn't be a cocktail without some alcohol, so be sure to get some. Here are some ideas for spirits you can use:
Clear or colorless spirits. These are more or less colorless in appearance and much of the time has a milder taste than other spirits. Colorless spirits include:
Vodka
Gin
(Unaged) Cachaça
Neutral Grain Spirit
Soju
Whiskeys. Whiskeys are made from fermented grain mash, with the grain used changing from type to type. Whiskey is popular around the world but primarily manufactured in Scotland, Ireland, America, Canada, and Japan, each of which have distinct flavors. The types of whiskey include:
Bourbon
Scotch
Rye
Irish
Canadian
Japanese
Other colored spirits. There are dozens of different kinds of spirits that would make sense in a cocktail. Some of the most popular spirits not to have already been listed include:
Tequila
Mezcal
Absinthe
Brandy

Add another type of alcohol to enhance the taste of the spirit, if desired.

Get a nice cocktail shaker.

In order to combine your ingredients together, you're probably going to need a cocktail shaker. Although certain cocktails that cocktails that use distilled spirits or very light mixers are stirred, most other cocktails are shaken.
Cocktails that have fruit juices, dairy products or eggs, simple syrup, sour mix, or any other thick ingredients should to shaken

Use a jigger or measuring cup.

A jigger is a useful tool if you want to make clean cocktails with exact measurements. Think about it: a cocktail where you "eyeball" the amount of alcohol or the amount of mixer can turn out too strong or too weak.
Many jiggers or measuring cups contain 2 sides, kind of like an hourglass. The small jigger usually holds 1 fl oz (30 mL) of liquid, while the bigger jigger holds 2 fl oz (59 mL). This makes pouring cocktails that require "double" shots much easier.

Muddle your fruit or herbs in the cocktail shaker first, if applicable.
Simply put the recommended amount of fruit and herbs in the bottom of your cocktail shaker and muddle with a muddler or the end of a wooden spoon. Make sure to get all the juices out of the fruit and break it up sufficiently.
Some recipes won't call for muddled fruits, but many will. A mojito, for example, calls for muddled limes and mint to begin with.

Add the juices, alcohols, and liqueurs into the cocktail shaker.
As directed by your recipe, add the required liquids to your cocktail shaker.

Put in the ice after adding the liquids.
Add ice once you're ready to shake so that you don't dilute the cocktail unnecessarily. This is a mistake that many people make. They put the ice in at the beginning instead of the end, thereby diluting their drink.

Close the cap to the cocktail shaker and shake vigorously.
This can take anywhere from 10 to 20 seconds, or until the shaker is too cold to hold. Vigorous shaking will combine all the ingredients in the drink together, blending them so that you don't taste an overwhelming amount of juice and not alcohol, or vice versa.
If you plan on salting or sugaring the rim of your glass — for a margarita, for example — do it now, before you pour the drink. Dip the glass into a shallow dish full of water, then dip it in a shallow dish of salt, sugar, or whatever is appropriate for your drink.

Add bitters to your drink, if applicable.
Bitters are aromatic flavorings added to many (usually whiskey) drinks after mixing. Probably the most famous bitters mix is Angostura bitters.

Finish with a garnish to your drink.
The garnish you choose should be suitable for your cocktail. An olive on a skewer, for example, traditionally goes with a martini.