Peel or not, as you choose. Break off the tips, but you don't have to string them. Slice long beans into manageable lengths, blanch them briefly and toss them with sesame oil or use just as you would a green bean. Andy Ta suggests stir-frying long beans with shrimp, garlic and bacon. Or braid them for a garnish, suggests Rosa Lo San Ross in Beyond Bok Choy, an excellent guide to Asian veggies.
Chinese celery looks like the Western kind, but with more leaves and smaller stalks.
Besides these familiar-seeming relatives of American favorites, try some of the other vegetables that you know from restaurants. Snow peas are one of the delicate glories of the Asian kitchen. You can eat young and tender ones raw, or steam them, saute with butter, or add to any stir-fry. Sometimes, the flat pods need stringing. Water chestnuts don't grow in cans.