Most drinks are strained after mixing or shaking. The Hawthorn style strainer is easy to use, but there are a couple of caveats. Starting out, be sure that the strainer sits easily on top of your mixing glass or tin. The spring should be at least a little compressed and the wings or back should be firmly on top of the container. The pros can stick a strainer down into the tin and not spill everywhere. I don’t suggest trying that at first. If your strainer is too small for the tin, pour the drink into the pint glass and strain from there into your chilled drink glass.
Sometimes you will want to double strain. To do this simply use the Hawthorne strainer and strain through a fine mesh strainer into the drink glass. Double straining removes ice shards and small bits of ingredients you don’t want floating in the drink.
You will occasionally want to filter ingredients before using them. Fruit juice that you want clear or when making syrups. You want to filter from large to small. Depending on how clear you want your liquid, you can stop with a fine mesh strainer or pass the liquid through a paper coffee filter. My progression is fine mesh strainer, then gold (metal) coffee filter, followed by paper filter.
If you are having trouble with a very fine slurry that plugs up the paper filter, try decanting. Put the liquid into an empty wine bottle and let it sit overnight or as long as possible. The slurry should collect on the bottom. Slowly decant the liquid into another container discarding the stuff at the bottom. Then try the paper filter.