There are two different but equally easy ways to pit cherries without a cherry pitter - the twist method and the poke method. You can use different tools to do each one, as discussed under each technique.
Choose fresh, ripe cherries. Rinse them with cool water, pat them dry, and remove their stems.
Note: If you have a lot of cherries, this is a good activity to do with a partner or two. If you're alone, settle in. This will take awhile. Listen to the radio, talk on a headset, watch television, or enjoy the meditative nature of a quiet, repetitive task.
You may also want to read All About Cherries to learn more about selecting, storing, and using cherries, or Cherry Varieties (or even Sweet Cherry Varieties) to learn more about the type of cherries you're using.