In the simplest of terms, a TA is a teaching assistant to a professor. The job entails assisting students, grading papers and assignments, teaching undergraduate classes, preparing classes/lectures for undergraduate students, administering exams, and helping the professor in day-to-day activities and related work. A professor does various other research activities apart from teaching classes. When occupied elsewhere, these professors choose eager and capable students to lessen the workload.
You can apply for the post of TA with your college application. However, you will be able to hold the post only after your first semester. Professors look for dedicated and eager students who wish to work long hours to give the desired result to the professor. After your first semester, go through the profiles and the work of professors from your course to find a compatible match.
Students often get a 50% or full tuition fee waiver. Apart from the tuition fee waiver, students earn an hourly stipend. The rate for the same is anywhere between $10/hour to $35/hour, depending on the department funding. You can expect to earn roughly $6000-$20,000 annually.