How to strain a cocktail
When straining a shaken drink, a Hawthorn strainer tends to be used, but when straining a stirred drink it is traditional to use a Julep strainer. Both designs of strainer allow the liquid to be poured from the shaker/mixing glass while retaining the spent ice.
Hawthorn strainers have a spring which runs around their circumference to help catch particles of ice and fruit created by the violent act of shaking. They also often have 'lugs' which rest on the rim of the shaker to hold the strainer in position when being used. Most designs of Hawthorn strainer incorporate a ridge or finger rest, which when pushed serves to secure the sprung-loaded gap between the strainer and the side of the shaker, so allowing finer particles to be caught.
Julep strainers are best described as being perforated metal spoons which fit inside the mixing glass. They are said to take their name from Kentucky gentlemen who would historically hold them over a Mint Julep to keep the ice and mint from their moustaches. Julep strainers are not as efficient at catching small fragments of ice as Hawthorn strainers but are more pleasing to use in conjunction with a mixing glass.