Drink plenty of water. Hydration is very important to maintaining vocal health in general. If your vocal chords aren't healthy, you won't be able to sing as high as you would like.
Breathe deeply from your stomach area before singing. Some refer to this as "diaphragm singing." The muscles in your abdomen support your vocal tone and can allow you to make higher notes sound stronger.
Open up your resonating chambers. Your voice resonates throughout your mouth, nose and throat. The back of the roof of your mouth should be raised as you sing, much like how your mouth would feel if you just about to yawn.
Relax and drop your jaw as you sing.
Visualize coming in from the top of the note that you are singing. Think about how the note should sound before you sing it and imagine yourself dropping in on top of the note. This helps you to have greater pitch accuracy and prevents flat notes better.
Warm your voice up gradually. Choose a sound such as "hee" or "hah" and slide your voice from a comfortable pitch higher and higher, but do so slowly. Sing softly at first and build volume as you go. If you try to sing too high and too loudly right away, you can injure your voice.
Sing every day. Just like an athlete must practice regularly to stay in shape, you must work your voice out regularly in order to train yourself to sing higher and better.