Sing vocal warm-ups beginning in the lower end of your range. Sing on the "ooh" sound and gradually change the "ooh" to "ah" as you get higher. Sing pentascales, meaning you will sing the first five notes of a major scale up and back down. Also sing arpeggios, which are the root, third and fifth of a chord. For each warm-up, continue the scales or arpeggios chromatically, meaning you go up a half step each time. Get an idea of how high or low you can sing and how high you want to extend your range.
Sing warm-ups by humming. Feel the air in your face, which is referred to as the "mask." If you do not feel vibrations in your mask, you are likely keeping your voice in your chest, which does not allow for resonance or good tone. Feeling the air in your mask also keeps your throat and vocal folds from going under too much strain.
Sing your warm-ups on "ooh" and "ah" vowels again, making sure you continue to feel the vibrations in your mask. Relax your jaw as you begin to sing high notes. Do not elongate your jaw too much or you will overextend your muscles. Think of the feeling of yawning as you open your mouth and the back of your throat and you will feel a rounding in the back of your mouth. You should not feel your throat because the resonant sound comes from the mask.
Open your throat more as you sing higher, using more air support. Do not squeeze the throat in an effort to hit the notes; air must come up to the head from a relaxed throat. Continue to sing chromatically until you reach the highest part of your range. Sing warm-ups just past the most comfortable high notes, but do not go too far. Do the same warm-ups daily and you will begin expanding your high range.