A good singing voice is said to come from what is known as "support". Support is a particular muscular state wherein the diaphragm and the ribs are pushing the air out of your lungs. Some people don't exhale 'properly', that is to say that as they exhale their belly goes outwards, the contraction of the rib cage does all the work. What should happen is a sort of rolling action where the diaphragm pushes upwards and your viscera roll in under the rib cage. This causes some reflex which closes the glottis bringing the vocal cords together. To get the glottis to close (which is what we do unconsciously to make a note) some people use the muscles which help them swallow. This is a mistake apparently, avoid this habit!
For good tone a vibrato is necessary. A vibrato (a waver in pitch) comes from being able to fine control the rate of expulsion of air, a vibrato's supposed to come from the diaphragm. That said, I've spent so long singing before I learned this that I do it by shaking my head! It looks slightly silly but I don't know for sure that it's a bad thing for tone or sustain. That said I want to learn to get a good vibrato using standard technique. Also people who can develop good vibrato are more agile at jumping pitches.
I have read that, with training, most people can cover a range of 3 octaves. This scares me, I can only manage 2 and a half and can't imagine how I might sing higher (a ridiculous falsetto) or lower than I do.