Exactly what method that is best suited to mix a certain drink depends upon the actual attributes of the liquids which is to be utilized in the particular drink. You essentially select method based on the drink. The actual mixing is meant to occur using the proper temperature. There are 4 different methods involved in creating drinks depending on the demands of the drink.
The most common way to make a drink is to make it in the glass you plan to drink out of. This method is simple but effective. It is primarily used when you have ingredients that easily mixes together. Built in glass is used mostly when there is one or two high alcohol ingredients involved. Or one part liquor and one part juice.
Drinks that are served chilled, in either pre-chilled glasses or with ice, is stirred in a mixer glass. It needs to be big enough to hold an ample quantity of ice to chill the drink without melting too much. You also mix liquors that are clear but gets cloudy if you shake them. You stir the ingredients using a bar spoon for about 20-30 seconds using circling motions downwards and up. After this is done you strain the drink through a strainer into the glass that you're going to serve the finished drink in. The ice that ends up in the mixing glass is thrown away.
Liquors, Syrups, liqueurs, milk and cream have different weights can only be mixed with intense motions. Therefore they belong in a cocktail shaker. You NEVER use any kind of liquids that contain bubbles, like sodas. Then you close the lid of the shaker and shake it firmly for about 10 seconds, 20 if it's a viscous ingredient or cream. You shake until the shaker starts to get condensation on the outside. After this it's time to strain the drink into the choosen glass.
Drinks containing ice cream, egg yolk or fresh fruit will be much better if blended in a blender. You pour/put the ingredients over the ice in the blender. You NEVER use any kinds of liquids that contain bubbles in a blender. If the Mixed drink you're making contains soda or any other liquid with bubbles you pour this into the glass after the blending is done. You always start the mixing process slowly and then increase the speed until the ingredients have mixed into a homogeneous liquid. After this is done you pour the finished concoction into the choosen glass.