Learning to breathe correctly and to control your breathing while singing is one of the most important things that a beginner can learn. It is very important to use all of your lung power when you are singing and not to run out of breath in the middle of a phrase -- meaning simply, you need to control the amount of air you push out with your diaphragm. Doing breathing exercises will help you learn to use your diaphragm and abdominal muscles while singing.
Lying flat on your back, place your hands around your waist, with your fingers pointing toward the center of your body. Focus on filling your stomach with air from the bottom to the top by taking a slow, deep breath. You should feel your stomach and chest rise, and your hands should be pushed outward. Breathe out slowly while you count to seven. Doing this two or three times per day will help you learn to control your air intake, as well as the air you expel, when you are singing.
Practicing your vocal scales on a regular basis will help you to become a better singer. It may seem a bit boring sometimes to sing single notes again and again, but doing so is very valuable practice. However, there is an even easier way to learn your notes. Simply play a single note on a piano or keyboard and match the pitch of the note with your voice. It doesn't matter what sound you make when you sing -- just try and duplicate the pitch. Go up or down the keyboard, matching the pitch of each note. This technique has long been considered effective by vocal teachers and coaches. It will also help you begin to learn and memorize what the notes sound like and the relationships between them.
Rhythm and timing is a huge part of being a good singer. Learning and thinking about rhythm can be done in a variety of ways. One simple way is to listen to the radio while you are in the car and count the beats. Notice when the singer stops and starts and count the beats in between. Count the beats between the verses and choruses.
When you practice your scales and notes at the piano, consider using a metronome at the same time. This will get you thinking about when you start and stop your phrases, which makes a tremendous difference when you are actually singing complete songs.