Both Diagon Alley (at US) and Hogsmeade (at IOA) have an Ollivander's shop where you are brought in by small groups to see a "wand pick the wizard" usually a youngster. After the show, everyone is herded into the wand shop, where you can browse and/or purchase a wand for yourself. The Ollivander's show is not required to purchase a wand, it's just a fun experience to see at least once, but I'd skip it if the lines are long outside or wait until evening when it's less crowded. The wand shops are small and get cramped since everyone is opening boxes to check out different style wands. If you want, you can go online and look at different character's wands which will save time when you go to purchase them. Hermione's wand seems to be a favorite as well as the Elder wand. My daughter and I didn't buy character wands, instead we opted for wands made of the wood associated with our birthday on the Celtic calendar, which I think JK Rowling did with at least some of the HP characters. We used google to find the calendar. There are several carts that sell all the wands, also Gregorovitch's Wand Shop in Diagon Alley, as well as the big Universal gift shops at the front of the parks, so you have plenty of choices when you want to buy.
Have a blast picking out your wand! Be sure to keep the box it comes in, the TSA has never bothered us as long as we pack it in the box.