How Can I Get Teaching Experience If My Institution Only Allows You To TA?

[cupparino]

and not teach your own stand alone course? (this is for a PhD program btw) 

[holographic universe]

some of my ideas (although its worth mentioning that my undergrad advisers have told me to focus on research first, and teaching can be learned on the job later, even if your objective is to land a spot at a small liberal arts college):

adjunct at nearby uni

adjunct at local community college

get involved in outreach/mentoring/advising at your uni (what I will do)

[cropop]

When I was a TA of a particular course, I was the only staff member the students ever saw and wrote all the lectures, etc.

However, there are also TAs for other courses that basically do nothing (maybe just office hours) or TAs that just grade.

It tends to mean different things for different courses.

[dr. t]

Usually, you teach sections. 

Universities with this restriction also generally have competitive opportunities for advanced students to give their own class.