Work on scales. Use monosyllabic letter-vowel combinations such as "do" and "mi" and sing them up and down through your chest voice --- your lowest voice and the one you speak in --- and your head voice, or your highest voice --- your falsetto. This technique smooths out breaks in your voice, helping you get from one end of your range to the other in one fluid motion.
Bend vowels. Singing is primarily holding and changing the way you form vowels. "Vowel bending" is when you work to change the formation of your mouth when singing high notes to help your voice systems, such as your throat and larynx, better accommodate them.
Keep an open throat and support your diaphragm while singing to give yourself the maximum amount of breath and lung strength to sing with.
Imitate others' voices. Sing along with people or recordings of people with a large range. You will not be able to match what they do all at once, but if you set certain songs or singers as benchmarks and slowly, gradually, in combination with the other techniques, work toward imitating them, you will have a standard against which to gauge your progress.
Maintain vocal health. What is good for your body is good for your voice and vice-versa. Keep your body healthy by drinking at least 64 ounces of water a day and avoiding caffeine and alcohol, as these dry out vocal tissues. If you do drink them, drinking an equal amount of water will counteract their effects. Avoid vocally abusive behaviors such as throat clearing, yelling, loud talking and coughing as much as possible. Also, on days when you must sing, avoid taking blood thinning medications such as aspirin, as these increase the risk of vocal bleeding.