How can I eliminate stress in a healthy manner?

Stay active. Exercise is a great way to relieve stress. Your body releases endorphins during exercise, which can help you feel calm. If you exercise 30 - 60 minutes a day, your stress levels can improve. When stressed, take 5 slow, deep breaths with your eyes closed, then roll your shoulders forward 5 times, then back 5 times. This will slow your heart rate and release tension in your neck and shoulders.
Various techniques. There is no way to fully "eliminate" stress, but there are proven ways to reduce it. A direct method is counseling, such as cognitive-behavioral therapy. Indirect methods include exercising 30-60 minutes daily, and having fun.