When you use your body weight for strength training, you not only build strength, you also improve your balance.
Gymnastics requires a great deal of upper body strength. While weightlifting is a valid option for building strength in your upper body, a better idea for gymnasts is to use bodyweight exercises. When you use your own bodyweight for strength training, you not only build strength, you also improve your balance. Start with three sets of 12 repetitions. And take one day of rest in between workouts.
Lie face down on the floor with your palms flat on the floor just wider than your shoulders. Push up onto the balls of your feet, straightening your arms completely. Pull your abdominal muscles in tight toward your spine. Keep your body completely straight from head to heels, as you lower your body toward the floor, bending your arms to a 90-degree angle.