Use your corners. Go deep in the corners and it will put more space between you and the horse in front of you if they are slower. But don't be afraid to pass if you need to, it's polite, then go right back on the rail.
That and just be killer slow at home. Get that hip moving around and your horse comfortable neck reining (if he's in a curb). I usually say I have to be twice as slow and collected at home to go a moderately slow rate at a show. The excitement will put the speed on if your horse isn't a seasoned show horse.
Take your time making transitions, I usually wait until the person in front of me has started (but don't take too long or the judges will be mad). Make sure your up and down transitions are flawless. Wear appropriate attire for western pleasure.
I dunno what else to tell you, there is a TON that goes into showing a pleasure horse, and even more just training it at home.
Novice riders tend to perch forward so my advice is to sit back and keep your head up, and do not mess with your horse's head throughout the class. It's called "checking and fixing" and will definitely affect your placings. Try to use your hips, legs, and spurs to guide your transitions and make everything look effortless.
Like others here have said, lots and lots of practice and transitions, but keeping the gaits clean and correct. Natural ability of your horse definitely helps as well.
If this is your first time doing WP, then I will assume you're entering a novice or "green" class. My advice will be tailored to that division. #1 - it's a pleasure class, so it should look like you're enjoying your ride and your horse should be a pleasure to ride. #2 - don't constantly look down at your horse's head, look to where you are going & don't pick at the horse with your reins. #3 - find a spot on the rail and ride deep into the corners, that way the judge can really see your horse. If you need to pass, do so safely and don't cut anyone off when going back to the rail. #4 - Have fun, when you can truly say you enjoyed your ride in a pleasure class, BEFORE the results are announced, you've nailed it.