Usually done with the help of a regular cocktail strainer (such as a Hawthorne strainer) for primary filtration and a smaller fine-mesh strainer for secondary filtration, double-straining your ...
Attach the Hawthorne strainer to the top and then pour the liquid into another ice filled cocktail shaker tin. Swap the Hawthorne strainer to the other tin and repeat the process 5 times to and fro.