The University of Michigan provides a pretty good break-down of their instructor composition:
http://www.collegefactual.com/colleges/university-of-michigan-ann-arbor/academic-life/faculty-composition/
Note that over 40% of all “instructional employees” are graduate assistants.
(“Ann Arbor has 1,856 instructional graduate assistants that teach or provide teaching-related duties. This could range from entirely teaching lower-level courses themselves, to assisting professors by developing teaching materials, preparing or giving exams and grading student work.”)
Your exposure to TAs may be especially high during your first two, foundational years.
Now, that’s Michigan (one of the best state universities in America, with a 12:1 student:faculty ratio). Imagine what you’ll get at an average large, public university in a state that doesn’t invest as heavily in education (and where the TAs may not be as good as the average grad student at Michigan).
These issues get a lot of debate on CC. Every applicant has a right to decide for oneself the importance of faculty composition and class sizes. IMO the OP is asking an important question (“how can you find out the percentage of classes taught by TAs at a college?”) Instead of only rehashing the broader debate (or trying to persuade us the question isn’t important) I wish we could identify good tools to answer it.