Most music students now study composition at schools and Universities. Sometimes imitatively, sometimes originally. Some have argued (Harrison Birtwistle for example) that composition cannot be taught. Some argue that, in a traditional way, the best way to learn is to learn imitate (Salvador Dalí said the way to learn to be an artist was to copy the great masters.) Others argue that encouragement and open-mindedness are best, leaving students to find their own voice.
What to study? Certainly hurdles and jumps can be set. Whether 'write a piece with only 3 pitches' or 'write a cabaret song in the style of Kurt Weill'. Perhaps underlying principles of form, characterisation, development, clarity and function of material within the music can be taught.
As well as the content of teaching composition coaching is an important aspect to consider. How to feed back, criticise, challenge, help the evolution of the music. Perhaps this is as much a human as a technical skill. And a challenge that many teachers are not prepared for in their training.