You just make matches, it's easy to pick up.
Some things to note:
Your score is based on the pieces you have on the screen, so if you match 5 purples (for example) your score will go down slightly since 1 leaf = 3 purples. That's OK, because it gives you more space for higher-level pieces.
Gold pieces don't disappear.
You can mix ingredients with recipes to get certain things.