Warming up will help improve your stamina allowing you to sing over longer periods of time. Involving the whole body helps take pressure of the vocal areas and helps you relax. It will also help you develop good habits, improve your singing range and technique.
There are various things that you can do:
Warming up the body
Sit on the edge of your chair, have a straight spine and put your weight on your toes. Breathe in naturally and fill your ribs expand out and up, make sure your shoulders are relaxed and down. Then breathe out with a sigh, then through pursed lips with your hands behind you and fingers on your hips, feel the back muscles in action.
You can work on the resonance of your sound through humming. Hum with your lips just touching but keep your teeth apart. Try this again, but with the sound ‘nn’ where you’ll find your tongue is half way back in your mouth and then the sound ‘ng’ with your tongue against the soft pallet. You should be able to feel the air resonating and then feel it move into your nose too. Try using nonsense words, and then other words like ‘sing’, ‘ring’ and ‘ding’.