How to do a vocal warm-up
Even before beginning to sing, you can prepare by thinking you are smelling a flower, which opens up the nostrils so that the sound you produce will be more focused. Also, really picture that the back of your mouth is really open and the larynx lifted.
Begin with gentle humming up the scale, beginning quite low depending on your voice type (bass, tenor, alto or soprano.) It is equally as important to warm up your lower register as it is your upper register. Next, sing up arpeggios to 'yah', which will really open the back of the throat. You need to try to recreate this open sound in all of your singing. Another exercise you can do singing up the arpeggio is using the words 'Bella senora'. On the final syllable, you fall down an octave from the top of the arpeggio to the bottom note (tonic.) You can find this on YouTube.
Sing again up the arpeggio but this time staccato 'ah - ah - ah - ah'. To really exercise your upper register, hold on to the top note for as long as you can.
When you are singing up arpeggios, it is important to try to create a level, even sound rather than creating the impression that you are really reaching up for the notes. To practice doing this, find a scarf and pull your hands along it in a straight line whilst you are singing. This skill will eventually transfer naturally to your main singing.
Another practical thing you can do when warming up is lay on the floor and place a book on your tummy in order to see how much you are working your diaphragm. You need to aim to see the book moving up and down as you take breaths right from your diaphragm. If you don't see any movement then it means that you are working your throat too much and not supporting your sound with the whole body. If you do this excessively, it can lead to a sore throat.