If you like painting standing up rather than sitting down, a palette is a very useful tool. It enables you to have your colors (and brushes) at an ergonomic working height and it's instantly accessible when you want to pick up a color or mix a color, whether you're standing in front of your painting or viewing it from a distance.
If you're using a traditional wooden palette, a plastic one, or a disposable paper one as in the photo, the principle is the same: use your forearm to support the weight of the palette. This stops your wrist having to hold the weight, and is far less tiring.
Insert your thumb through the hole, then curl your fingers around the edge or just rest the palette on top of them. Hold it firmly, but not in a panic-grip. You don't want to get cramp in your fingers, you just want to be sure you don't drop the palette when you put brush to paint.
Be careful you accidentally don't lean into the paint on your palette. It's easy to do if you bend over to pick up a brush you've dropped, for instance.