This is a crucial question. Overall it depends on the context where the teacher works:
1) What does the law say?
2) What training do teachers get about it?
3) What possibilities does the school and context provide?
This differs from country to country I think.
In Greece, if teachers notice such an issue (or e.g. a learning difficulty), they refer to head-teacher, school coordinator, parent. Then, they may refer to other institutes which deal with those.
In some cases, there another educator (special education teacher) may get in the classroom to assist.
In modern days, teachers tend to be the responsible and knowledge adults that passes most of the day with the kids. The problem is that they do not receive any certification or course to make possible to identify and support someone with an alteration of their mental health.