Look for dark greens leaves of a uniform color. Avoid yellowing leaves, damages leaves, wilted leaves, or excessively moist-looking leaves. A bit of dirt is fine - it is likely the result of recent rain or watering (splashing dirt up onto the leaves).
Note: Arugula is sold either by the bunch or as loose leaves (much like spinach). In general bunched arugula has larger leaves and loose-leaf arugula has smaller leaves.
Bunched arugula needs to have its tough stems removed and discarded before cleaning. Arugula is best cleaned in a large bowl or basin of cool water. Gently swish leaves in the water, letting any dirt fall to the bottom of the bowl. Lift clean leaves out of the water and transfer to a salad spinner or several layers of paper towels or a clean kitchen towel. Dry in the spinner or by rolling in the towels. Transfer leaves to a layer or two of paper towels (or clean, dry ones if you dried the leaves with towels), gently roll them up, and store in a loosely closed plastic bag in the fridge. (See this Step-by-Step Guide to Cleaning & Storing Greens for pictures.)
Arugula stored this way will last up to a week. Uncleaned leaves keep about 3 days.
Different Arugula Leaves For Different Recipes
Smaller arugula leaves tend to be milder, while larger leaves tend to have a more aggressive, peppery kick. They are great in salads on their own or combined with other lettuces.
Wild arugula - sometimes available from foragers in the late spring and again in the fall in temperate regions - is much more peppery than most cultivated leaves. It's perfect for using as a garnish, since just a few leaves give plenty of kick, and other raw preparations where its intense flavor can be appreciated.
Larger arugula leaves tend to have a stronger flavor, so they can be cooked successfully without losing all their flavor or used raw by those who like its assertive flavor.
Arugula Salad Recipes
Arugula adds a peppery kick to salads of all sorts, pairing particularly well with sweet mild lettuces like Boston (a.k.a. butter lettuce) and Bibb lettuces. Dressings made with olive oil and balsamic vinegar highlight the bold flavor of arugula, as do lemon juice-based dressings. Here are a few of my favorite arugula-specific salads: