This is one of the most important skills to learn and get down. Seriously consider practicing this early on. Just picture this, you're out on your new stilts. You've attracted a crowd, then WHOAH! you fall. There goes your dignity. But WAIT! You can somewhat regain it back by getting up WITHOUT the help of your laughing friends.
This took me a few tries to learn. Plan to fall while doing this. Please, please wear proper safety gear, helmet, wrist guards, elbow, and knee pads.
Basically, you get on both knees leaning forward. Put your strongest leg up front, with the hoof on the ground and your knee bent. Pull it close to you, and lean your weight over it. Use a hand to grip it if needed. Push up from that leg, as you do pop your other leg around and then land on both feet.
Sounds and looks easier than it is. But eventually you'll get it down. Practice, practice, practice and eventually you'll pop up from the ground without even thinking about it.
Need more visual help? I personally learned from watching this video by BalthezarArith