Summarize:

The first exercise to begin with when attempting to improve your balance is the weight shift. This is exactly what it sounds like - shifting your weight from one foot to the other. Stand with your feet one hip width apart. Try to distribute your weight evenly over both feet. Now, shift your weight so that you are balancing on your right foot only and lift your left foot just slightly off the floor. Hold this position - balancing on one foot - for as long as you can while remaining steady. Aim to reach 30 seconds. Lower your left leg and stand on both feet again. Now repeat the exercise, this time balancing on your left foot. Repeat 3 or 4 times on each leg, and practice the exercise everyday until you can easily balance for 30 seconds on each leg. This exercise is the natural progression from the weight shifting exercise. It is performed in the exact same way, except this time: When you balance on your right foot, lift your left leg and bend it backwards at the knee. Try to hold for 30 seconds, before repeating on the other leg. If you want to make this exercise more challenging, consider balancing on a pillow or thick rug - this provides more of an unstable surface and makes balancing more difficult. For this exercise, you will need a single dumbbell - the weight depends on your own personal preference, but somewhere between 5 and 15 pounds is good for starting off. Stand with your feet hip-width apart and hold the dumbbell in your left hand at waist level, with the palm facing upwards. Shift your weight onto your left foot and lift your right foot off the ground, bending your leg forwards from the knee. Perform a set of 5 - 15 bicep curls, depending on how long you can hold your balance for. Repeat with the opposite arm and leg. This exercise is similar to the previous one and will also require the use of a dumbbell to perform. Stand with your feet hip-width apart and your weight evenly distributed. Hold the dumbbell in your left hand. Lift the dumbbell upwards toward the ceiling, until your forearm is perpendicular to the floor. Now lift your right foot off the ground and bend your knee backwards. Try to hold this position for 30 seconds without losing your balance. Repeat holding the dumbbell in your right hand and balancing on your left leg. This exercise tests your ability to walk in a straight line without wobbling or losing your balance. If practiced on a daily basis, it can help with your coordination and allow you to improve your balance. Find a straight line on the ground. It could be the crack between the tiles in your kitchen, or a painted line in a children's playground. You could even make your own using a length of sticky tape. Now try to walk along the line, one front in front of the other, without falling sideways. The first couple of times you can extend your arms out to the sides (like airplane wings) to help you balance. Next try doing it it with your arms pinned to your sides. And once you've mastered that, try walking backwards. Finally, try walking along the line with your eyes closed - tricky, but not impossible!
Try weight shifts. Try leg lifts. Try one-legged bicep curls. Try one-legged shoulder presses. Walk the line.