The way they are usually prepared in Southwest China is the following:
Wash them and clip off the little curly bits with your fingers. Heat up a wok with some oil in it. Fry some chopped garlic (and if you like it spicy, some dried chilis) in the hot oil for just a minute or so before you add the pea shoots. Sprinkle some salt over it (or use chicken broth powder). Stir quickly on good heat for just a couple of minutes (until the pea shoots start to get soft - but you don't want to cook them mushy!). Serve and enjoy!