This is a pretty common question, especially from young people who are realising they're not too young to be affected by mental health issues.
My answer is generally along the lines of "honestly, I'm not entirely sure". Which is true. It's pretty difficult to pinpoint when things become more than just "teen angst". The one thing I do know is I was 13 when it became pretty clear to me that things weren't right. I was self harming, experiencing incredibly low self-worth, and attending school was becoming a near impossible feat.
So the easiest thing to do is to point out that everyone's experience is different. Just because I became aware that I was ill at the age of 13, doesn't mean that someone else will notice at the same age. They could be younger, or older.
The only practical advice I can give is to watch out for changes such as going from full attendance at school, to being late on a regular basis, or skipping days because getting out of bed just seems impossible. Or getting breathless on the bus to school. Going from being social to avoiding interaction with people at all costs. Grades falling, and of course, the standard losing interest in things you once enjoyed.
Sometimes these are signs of something more sinister than becoming introverted, or rebellious, or a shift in interests. Sometimes these are signs of a mental illness.