Warms up should warm up the body, the brain, the voice and the breath.
You should also make sure you are properly hydrated with lukewarm water or some warm tea. Coffee dehydrates the voice and fizzy drinks can cause you to burp. Do not drink ice cold drinks as that shrinks and tightens the muscles around your throat and we want them nice and relaxed.
How do we warm up?
The body can just be moved and stretched a little. Shake your legs and arms out, do some shoulder rolls and shrugs, look from left to right and up and down. Stretch up, round and forward with both hands, circle your hips and ankles. If you can do something to raise your heart rate just a little then that will help circulate the blood around the body better.
The brain is best warmed up by doing something mentally stimulating like a tongue twister or anything that is a little silly and makes you laugh. This of course also helps warm up the body and the breath. A good laugh is great for getting the belly muscles engaged which then in turn helps control the diaphragm.
The breath is warmed up by relaxing your belly, (SPLAT), take in some air and engage your lower abdominal muscles to control the escaping air as well as keeping your ribcage lifted. You can set a timer to see how long you can make the out breath last and aim to increase that time. Whenever you feel the need to breathe out fully focus on pulling in your abdominals and keeping the ribcage expanded then breathe out.
Warm your voice up with a few scales on the vowels ; ee, ay, ah, oh, oo. Prepare the breath, consider the shape of the vowels and how much space they need in your mouth. Each vowel needs a different amount of space and has a different shape and each note requires a different amount of space.
For singing we mostly need to breath in for no more than 4 counts and then allow it out with control. You can use a straw in a glass of water to see how steady your escaping air is. This exercise also helps to create a slight back pressure on the vocal folds which in turn makes them close more cleanly and thus give a better clearer sound. This exercise is also good for the ageing and weakening voice. The deeper the water and the deeper you insert the straw in the water, the more back pressure you create and the depth of water will make it hard to create a steady flow of bubbles which in turn requires you to focus more on the exercise.
Exercise
Try the straw in a glass of water and see if you think it helps your breath control and the sound of your voice.