Generally when they say 'teaching' the vast majority if universities actually mean 'demonstrating' (or at least in my experience anyway, somebody may correct me!). For example, in the sciences, it is common for the PhD students to supervise the practical sessions, rather than do any actual teaching, i.e. they do not give lectures. In addition, PhD students may also run seminars with small groups of students. You will not need any formal qualifications for this, although your uni may run a few training sessions to get you started.
As I say, other people may have different experiences, but I have never heard of a PhD student taking lectures as such.