Mixing
Different recipes require different ways of mixing your drink: shaking, stirring, floating or layering, muddling and blending.
Stirring
To stir properly, use gentle motions with a spoon to ensure no cracks in the ice cause the cocktail to be diluted with water or for too much air to be incorporated into the drink.
Shaking
Shaking is the most dynamic way to mix your cocktails and fun for everyone to watch. However its real purpose is to chill ingredients while they are being mixed.
Ensure you have enough ice in your shaker, usually around 3/4 full, and shake it long enough with enough varying motion so that the ice circulates well to help mix the contents. You can tell the contents are chilled enough if there is condensation on the shaker and there is a small amount of foam which appears at the top of your drinks when you pour.
Layering and Floating
Layering is usually used for making shots such as B-52s. You basically float each layer of your ingredients from densest liquid at the bottom to lightest liquid at the top.
An easy way to do this is after pouring the first layer into the glass, use the back of a bar or tea spoon to gently pour each successive ingredient without breaking the previous layer. You can slow down the flow further by bracing the spoon against the inside of the glass.
Muddling
Muddling is used in drinks like the Caipirinha to roughly mix fresh ingredients such as lime wedges with others such as cane syrup before the alcohol is poured.
Basically you put the ingredients in a glass or other container and use the back of a spoon or a pestle to crush and extract the flavors.