If you don't want to buy one of the various moisture-retaining palettes available at art stores, it's quite simple to make your own. The advantage (besides cost) is that you can use a container that's the exact size you want, rather than having to make do with the sizes available.
What You Need:
A shallow plastic container with a tight-fitting lid, such as a food-storage container or lunchbox. It doesn't matter what shape it is, but look for one that's quite shallow rather than deep.
A piece of watercolour paper. It doesn't matter what kind, though a thicker sheet works best as it holds more water.
Greaseproof paper (baking parchment). Buy a roll, because you'll replace this every time you clean your palette.
A pencil.
Scissors.
What You Do:
Cut a piece of watercolour paper to fit in the bottom of the plastic container. The easiest way to get a good fit is to place the plastic container on the sheet of watercolour paper, trace around it with the pencil, then cut just inside the line.
Cut a piece of greaseproof paper the same size.
Soak the piece of watercolour paper in clean water, then put it in the bottom of the plastic container.
Moisten the sheet of greaseproof paper and put it on top of the sheet of watercolour paper.
Squeeze out your acrylic paints onto the greaseproof paper and start painting.
When you've finished a painting session, simply put on the lid of the container to keep the acrylics moist until you next pick up your brushes.
Tips:
If you haven't got a suitable plastic container, you can use a baking tray or deep plate and plastic film instead. The disadvantage of using plastic film rather than a stiff plastic lid is that it's likely to touch the paint and so be more messy to take off and replace.
If the sheet of watercolour paper begins to dry out, lift one corner, pour in a teaspoon or two of water underneath, then gently tip the palette so the water runs under the paper.
If you cut the piece of greaseproof paper slightly smaller than the piece of watercolour paper, you needn't lift the sheets to remoisten the watercolour paper.
How Do I Use the Palette?
See: How to Use a Moisture-Retaining Palette for Acrylic Painting.