They use cells called chromatophores to change their color. These can be yellow, red, white, black, brown, or blue. For some animals, these cells are pretty much stationary, but some have the ability to squeeze one end of the cell, causing it to either bulge a the top so it is visible, or bulge at the bottom so it is hidden.

If you want to imagine that easily, get a long balloon and fill it partially with water. If you squeeze the top, all the water (which simulates the pigment in the cell) goes to the bottom. If you squeeze the bottom, the water goes to the top, where it would be visible on the skin of the frog.

By controlling this, they can change their color, blending the colors to produce many different shades. Some creatures use this for camouflage, while others change due to temperature or level of excitement.