The first step to being a better singer is to learn proper breathing technique. As a singer, the best way to breathe is from the diaphragm, not from the chest. The reason being, by doing this you are able to fill your lungs with more air. This will enable you to sustain notes longer, and will also allow you to prepare for vocal warm ups. Breathing should be slow and steady, and this should be practiced all day long, not just when singing. For a singer, this way of breathing should be constant.
The next step is to work on how the air is going to be expelled from the lungs through the folds of the vocal chords. The first exercise that can help you practice this is one called "lip rolls." With the lip roll exercise, the lips are gently placed together, and then the air is expelled almost like a baby doing a "raspberry" if you will. It is not that easy to do and must be practiced efficiently before moving on to the next exercise.
Third, one should use the lip roll exercise and apply it to a musical scale. The air should be expelled while almost "humming" the note of the scale, slowly progressing up the scale, and then back down.
After the previous exercise, one can proceed with the "shhhh" exercise. IN doing this, you breathe in deeply from the diaphragm, and then expel the air in a harsh "shhhhh" sound and let all the air out slowly.
The above exercises may seem silly, but they will not only help improve your vocal range, but will also act as warm ups so you will have less stress on your vocal chords, and will be able to sing across registers more easily.