The short answer would be "With some difficulty". If you are an instrumentalist, ask yourself, how would I practise if I didn't have my instrument with me? That puts you, more or less, in the position of a singer.
Ordinarily, I imagine that bassoonists, say, practice by by getting the instrument out of the case; then they get the music out, and put it on the stand, play through some scales and pieces, and perhaps repeat a few bits.
Singers can't do any of the normal instrumental practice stuff. Largely, if they know the song already, then they can sing it, if they don't, then they can't. Some singers who are also instrumentalists can play the vocal line of a song, but most can't - or at least can't play it adequately with accurate rhythm and notes. I may have sufficient skills to work out pitches in a difficult melody line with a score and a tuning fork, but that is an advanced skill, which I wouldn't expect school-age students to have. I give my students recordings, and backing tracks to help, but I am aware that it is a distant second best to them being able to work out the line for themselves.
There is a further issue of self-consciousness here: especially if practice involves looking in the mirror, as it should.
So what is left? Singers can memorise songs that they know, especially the words.
But most importantly, what singers can do is practise the voice. I give all my students warm-up exercises with backing tracks so they they can work on the five main areas:
- Breathing - in and out
- Diction - vowels and consonants
and sometimes, extra exercises for things like reducing tension, or singing across the break.
That seems to me to be the best route to improved vocal skills, and establish a practice routine.