Arugula is often grouped with other strong-flavored greens, especially watercress and dandelions, but its distinctive, strong flavor is all its own. Certain words are frequently used to describe arugula (which is also called rocket, about as good a name as you can imagine for a food): peppery, mustardy, spicy-but you have to combine all of these (along with the word "rocket") to really capture arugula's unique sharpness.
Arugula is also sometimes described as "elitist," but that's ridiculous: it's a democratic weed, will grow in your garden almost as fast as you can pick it, and is now available almost everywhere in the country. Besides, when Paula Deen and Rachael Ray have recipes calling for a certain ingredient, and when it starts showing up in McDonald's salads, I think you can pretty safely call it mainstream.
Whether you're shopping at a grocery store, buying from a farmer's market, or picking from your own garden, use the same criteria for choosing arugula as you would for any other leafy green: Go for unblemished, sprightly, deeply colored leaves. Arugula is relatively fragile and perishable, so either use it within a couple of days of buying it (maybe you can extend "couple" to "few" if it's super-fresh to begin with), or extend its shelf life by sticking its stem end in a glass of water and covering the whole thing with a plastic bag.
There's no denying that a bowl of fresh arugula with a drizzle of olive oil, a squeeze of lemon, and a sprinkle of salt and pepper is a real pleasure. Simplest thing in the world, and among the best. What doesn't make sense to me, though, is combining arugula with milder greens like loose-leaf lettuce and spinach -- arugula just blows them away. Instead, when I'm adding ingredients to arugula salad, I tend to favor assertive flavors that stand up to and complement the green's bitterness. Sweet, juicy strawberries and tart, winy balsamic vinegar fit the bill perfectly, which is why I turn to this simple salad summer after summer. (For best results, use really good balsamic vinegar here -- look for the words "Aceto Balsamico Tradizionale di Modena" on the label.)
And you have plenty of other options for arugula salads: Salty ingredients like capers, sardines, olives, tuna, and Parmesan have a nice way of balancing out arugula's earthiness. Citrus fruits, especially slightly sweet ones like orange and grapefruit, are another good option, as are sweet-yet-acidic tomatoes. For textural contract, beans (think white beans and chickpeas) and nuts (especially almonds, hazelnuts, and pine nuts) are lovely. And I find that fresh parsley and basil have a surprising chemistry with arugula. Feel free to experiment, but use your judgment and keep the number of additions to no more than two or three: Too many salads are ruined by a jumble of discordant flavors. And you don't want to hide the arugula.
And arugula has many uses beyond salads: you can use it almost anywhere else you would use greens like spinach, escarole, and chard. I love adding arugula to pasta dishes, as is done throughout Italy (and, for that matter, California); it wilts in the heat of the pasta and is a nice foil for pasta-sauce ingredients like garlic, tomatoes, and creamy cheeses. You can also use arugula in vegetable and bean soups: Chop it roughly, stir it in at the last minute, and keep the pot on the heat until the arugula wilts, just a minute or two.
My new favorite thing to do with arugula is to turn it into chimichurri, that garlicky, vinegary Latin American green sauce usually made with parsley. I've been making arugula pesto for ages, but this paste is brighter and not as rich-perfect in summer. Both arugula and chimichurri have an affinity for smoky grilled meats and vegetables; try spooning it over simply seasoned chicken or pork kebabs or grilled zucchini or mushrooms. Or stir it into cooked rice or grains for a flavor boost, dribble it on top of poached fish, or serve it as a dip with crudités and baguette slices.