The Boston Shaker is used to mix as well as chill the drink ingredients. It's got two parts: a flexible metal tin and a mixing glass. Fill ice and liquids in the mixing glass. Put fit the tin part on top and press lightly to form a seal. Shake it up. You need an additional strainer to trickle the mixed drink into a glass.
The Hawthorne strainer
The Hawthorne usually has a spiral on the edge to keep ice cubes and fruit lumps out of your drinks. When you buy a shaker, it often comes with a strainer. In a pinch, an everyday kitchen strainer works as well.