Snap peas (top left in the photo) can be eaten whole, except for the stem, and do not need to be peeled. Their shells are thick and juicy and the peas inside should be plump. They can be eaten raw, chopped for salads or stir-fries, or sauteed lightly. They don't benefit from long cooking.
Shell peas (top right) have tough, inedible pods and delicious little peas inside. These are the peas you find frozen in bags at the supermarket. We find the best way to open the shells is to pull the stem backward, down the side of the pea that curves inward with a slight indentation. This unzips the pod, which you should be able to easily open to scoop out the peas. These can then be eaten raw, or steamed for 5-10 minutes, depending on how you like them. Topped with butter, salt, and pepper, they're pretty amazing just like that! You can blanch them in boiling water for about 2 minutes and freeze.
Snow peas (bottom) are also edible-podded peas. In fact, the pod is most of the action in a snow pea; the peas inside are usually quite small. Like snap peas, they are good eaten raw, but are probably most well-known in stir fries and other Chinese dishes. They can be sauteed or steamed, just briefly, or added to salads. A quick, tasty side dish can be made by sauteing snow peas in sesame oil for just a minute or two, then tossing with lemon juice, salt and pepper.
Because fresh peas are so good, and the season so short, we tend to prepare them in simple ways that really highlight their own flavor (ie, sauee for a minute and add butter). But, of course, there are lots of options to incorporate peas into many other dishes - here are some ideas for snap, shell, and snow peas.