Every so often, drop your thread and let it untwist.
Or, try this: When sewing by hand, the natural tendency (although we don't realize we're doing it) is to roll the needle between our fingers as we stitch, causing the thread to twist. If you are right handed, typically, the needle is rolled in a clockwise direction. As you are pulling the needle through to complete the stitch, roll it in the opposite direction to keep the thread from twisting. Naturally, you will want to verify the direction of your twist so you know how you need to compensate.
Another thing that helps is to run your hand sewing thread through a chunk of paraffin wax to coat it, but there are also other types of thread conditioners on the market if paraffin is not available.