You can give your Westie all kinds of hairstyles, from American Kennel Club show-approved cuts to a cute and manageable puppy cut. Your pup won't mind what his hair looks like, so pick a style that you think suits him.
Westies are naturally double-coated, with a hard, straight outer coat and a softer undercoat. If you like the look of your pup with his natural coat, there's no reason you should give him a trim. You'll need to brush him daily, though, to keep his hair free from matting and to help him shed his undercoat. You may need to trim the hair around his eyes now and then, so it doesn't get in his way.
Some Westie owners swear by hand-stripping, rather than clipping, to get the best coat texture and quality. It will usually make your pup's hair harder and coarser, which is especially desirable in show dogs. If your dog is just a family companion, it's probably unnecessary to have his coat stripped -- but the choice is yours. Always let an experienced groomer hand-strip a Westie.
A puppy cut is a coat cut to one length all over. You can choose the length according to what you think looks best, but it's usually cut to between a half-inch and 1 inch. The hair on your Westie's face can be trimmed short or left longer, depending on your preference. This cut is low-maintenance, so it's perfect if you don't have time for daily brushing sessions.
If you want to compete in the show ring with your Westie, he'll need to have an AKC-approved hairstyle. The AKC breed standard states that the coat should be around 2 inches long except shorter on his neck and back. It should be trimmed so longer areas neatly blend into shorter areas and furnishings. The hair on his head should be hand-stripped to give a rounded appearance. His coat should be hard and straight -- a soft or silky coat is a major fault.