To learn to sing on pitch, sing into a tuner. Sing a phrase, and every once in a while hold a note long enough that it registers on the tuner. Check if you are still on key. Obviously, this is for practicing, not for performing. It made a huge difference for me!

The tuner has to be the kind with a microphone for this to work.

Also, if you accompany yourself with a guitar, ALWAYS tune it before you sing and tune it often between songs. When you hear only true notes, your ear will start to demand them from your throat.