Straining paint and mixing paint together (boxing) are key to a great paint job. Once you strain a gallon of paint you will see why. It is amazing how much stuff is sometimes in there that shouldn’t be. There does appear to be a correlation between the price (quality) of the paint and how much gunk can be strained out.
We use paint strainers like the one above. You can purchase these at any paint store. They work great and are not very expensive. They go into and drape down over the sides of a 5 gallon bucket. The only real down side is you have to monitor them. They will pull themselves down into the bucket. You also have to pull them up and out of the bucket and hold them until they drain all the paint out of them.
We made our own type of strainer using a bucket and some window screen. We initially did this because we had plenty of both available but soon discovered how well it works. What we did was take the lid and cut the center out of it with a jigsaw. You want a big ring. Just the edge or lip of the lid all the way around. Then all you do is take some screen and push it down a bit into the bucket so you form a bowl of screen. Then put whats left of the lid, (the ring) on the bucket and press it down to hold the screen. You just pour your paint onto the screen and it does the rest. You don’t have to stand there and monitor it and when it’s all strained all you need do is hose off/rinse the screen and you are ready for the next time.