If they lean seriously inward, you're probably a pronator. If they only lean in somewhat or appear to be primarily upright, your probably neutral. If they seem to be pulling or collapsing outward, you're probably a supinator. Pronators should purchase a shoe with motion control in the midsole to keep their natural tendency toward rolling inward in check. Supinators should look for shoes constructed with maximum ankle and heel support.
Neutral walkers can run away with just about any well-constructed walking shoe.
Since your feet are you most valuable resource for walking, make smart shoe purchases. You can buy high-quality shoes in department stores or in discount stores, but you'll lose the expert advice you'll find at stores that focus on walking and running. Most specialty stores will let you take your shoes for a test walk, so take advantage of it. When you really get going with your rocking-walking motion, you'll likely be striking the ground hardest on your heel, which is why you'll want good cushioning there in your shoe. As your foot rocks forward, you need a flexible forefoot to allow for full extension of your stride.