Practice sightreading. If you don't know what that is, it's reading music that you've never seen before and singing it. It helps to make you sing on pitch.
Also, I suggest learning a little about music theory so that you always know what is going on in the peice. Is there a crescendo? Mezzo di voce? A ritardando at the end? What is the tempo? If you can't answer these questions, a brush-up on music theory is in order.
Get a straw. Sit up straight, and have your feet on the floor-one slightly in front of the other. Try to do this in front of a mirror. Place the sraw in your mouth, and breathe in through the straw. Your back should widen as you breathe in, but your chest should not rise very much at all.
Say "sqeelo" (skweeloh) with an italian accent on one note and then move up and up until you hit the top of your range.
Sing, " Bumble bee-ee bumble bee-ee bumble bee-ee bumble-bee." Play this on the piano, starting on middle C, and play CE DF EG FA GB AC BD C. Play the notes similar to that pattern coming back down the scale.
Go to the higher part of your range and sing, " Ee-ooh-ee-ooh-ee-ee-ee-ee-ee-ee," legato, full voice.
I highly recommend the book Singing for Dummies available at Borders and at Barnes and Noble. It comes with a CD that is really great with warm-ups, which are always good to practice.
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