Just as you can build your upper body strength in order to hold Forearm Stand, or increase your flexibility so you can do Wheel Pose, you can also improve your balance in order to master poses like Tree. The best way to feel confident is to practice poses that challenge your sense of balance: here's a yoga sequence that involves mostly one-legged standing poses. Bonus — this yoga sequence will also give you sexy, sculpted legs. First follow the sequence through on the right side and then repeat on the left.
The trick to standing on one leg is to concentrate on your breath, move slowly, focus your drishti (your gaze) on one point to help you feel grounded, and engage your standing leg and abs to help stabilize your body. If you find you're tipping over or falling out of a pose, just take a deep breath and try again!