With their growing bodies, kids already tend to struggle with their balance -- so it's no wonder they can be wobbly on a pair of roller skates. They may grow out of it, but if you're the one with the balance issues, you have less of an excuse. You might have to spend some time working on your balance before you head out to the rink.
Most people are more agile on one foot, so the first thing you should do is test your balance on both sides. The simplest way to do this is to do a simple standing test. Have a clock with a second hand nearby so you can time yourself as you stand on one foot, with the other foot raised and resting against your ankle. You should find that you're able to stand on one foot longer than the other. Whichever side is weaker, do twice as many exercises with that weak foot.
One Foot Stand
The test you did is also one of the easiest ways to improve your balance. Whenever you're standing around, such as when you're working in the kitchen -- without knives, of course -- or when you're watching TV, practice standing on one foot. As you get more agile, move your foot higher up on your leg. Start near the ankle, then move up to the calf, and progress to closer to the knee. Also try holding one foot out to the side and leaning slightly in the direction of the foot on the ground, which will further challenge your body to hold itself in balance. Over time you should start to notice that you're able to hold each pose longer. Balancing on one foot is a key skill for skating.
Another way to improve your balance while you're not actually in your skates is to use a wobble board, essentially a solid ball surrounded by a flat, round wooden board. If you don't want to buy one, check at your local gym. Start near a wall when you first try this. Step onto the board, placing your feet on either side of the ball, and hold the wall with one hand. Practice just standing on the board to start, letting go of the wall when you can. As you get more balance, let go of the board. As you get even more balance over time, practice tipping the board from one side of your body to the other, and then forward and backward, allowing it to tip just above the floor.
On the Rink
Achieving balance while you're on the rink is going to take practice; the more you skate, the easier it's going to get. Start with your skate bearings set tight, so that they don't roll fast. Stay near a wall or a hand hold, or if you need to, ask the ring workers to give you a contraption that looks like a walker that you can use to gain confidence. As you skate, practice the "duck" motion, in which you keep your heels fairly close together as you push off and glide. Stay low, bending your knees and keeping your butt close to the ground, as that will help you prevent falls. As with anything, practice makes perfect. Another word of warning: Broken bones are always a risk when you're roller skating -- either from falling or from suffering a collision with another skater. If you're over 50, your risk of osteoporosis is higher, and thus too your risk of brittle or easily-broken bones. Some things you can do: exercise regularly, eat lots of fruits and vegetables and be sure you're getting enough calcium and vitamin D. And of course, use extreme caution when learning the ropes of skating.