Schedule your trip around dates that are not peak tourist travel times. Granted, this may difficult if there are work and school schedules involved, but if you can, it would be advisable as much as possible. The Harry Potter park will not only attract US tourists but also many tourist from the UK and everywhere else, so, keep that in mind when planning your trip there.
Get a map of the park. Plan your days around what you want to see and ride. It's important to have a plan. Understand where you would need to park if you are driving and also, the distance from your hotel or dwelling from the park and how long it will take you to get there. Also, take note of opening and closing times so you can plan your day around that as well.
Arrive early to the Harry Potter park. Like the saying goes, "the early bird gets the worm". It may not always be fun waking up early, but once you get there, it will be worth it. If you're one of the first people there, you can get to the rides first, the shops and eateries as well. Sure, it may get crowded quickly, but if you can shave some time off by getting there early, that would help everyone in your group have more time to enjoy the park.
Caculate time for eating and shopping as well. This is definitely something you would want to take part of. Of course, you can always schedule time for browsing in between rides, or you can set specific times dedicated to shopping / window shopping as well as eating. Also, calculate how much time you want to spend taking pictures. Everyone wants to take pictures, especially at a place such as the Harry Potter park. There will be many photo and video opportunities. Understand this will slow down your pace as well as the pace of others if you have to ask people to move so you can take a picture or if you're in line and you halt it to take a picture or video, so, calculate time for that into your schedule too.
Create a budget and stick to it. One of the easiest things to do at any park is spend money on everything and anything you see. There will be many temptations as everything is new at the Harry Potter park, but you should create a budget and stick to it. Of course, you want to try and buy everything, but not everyone can do that. Save up your money and create a budget for food and shopping that will keep people happy without getting out of line. If you can afford the basics, stick with that and enjoy! If you can afford more, great, but don't let things get out of hand, that only causes misery in the end especially if you come back with things you find out you didn't really want or need later. Furthermore, there are many cost-effective ways to enjoy time at a theme park anyhow. You don't have to try every item on every menu at every eatery to enjoy the feel of the park and you don't have to purchase everything at every shop either. The experience of the surroundings, the sights and even window shopping can be just as, if not more fun!
Ask for any discounts and coupons that you can get. If you can get a corporate discount that is great! If you can get a senior discount, super! If you can get free parking passes if you're driving or any complimentary meals, buy one get one free, etc...All of those things are good. Save your money, don't spend if you have coupons and discounts available there for you! You can look online, ask your booking agent, talk to your hotel manager, there are many, many ways to find deals especially at a new park.
Enjoy your trip to the Harry Potter park. Make the plan something you and your travel companions will enjoy. Don't create a plan just to have a plan if you feel it will take the fun out of it. If you don't want to ride every ride, then don't. If you do, find the most time efficient way to do so. If you don't want to eat at the park, then don't. The point is, it's your trip, your plan should revolve around what you and your party will like the most. In the end, that is what will make it most enjoyable and memorable for you.