As an undergraduate at the University of Colorado, I was a Learning Assistant (LA) during my second semester, helping out in an intro-astronomy class I had completed my first semester. My primary duty was to help students work through labs (during recitation section). Throughout the semester, all first-time Learning Assistants took a class focused on how to engage students and increase retention, and throughout the semester, I would (attempt to) apply what I had learned in that class to the recitation in which I helped students.
I also tutored physics for a semester and graded astronomy homeworks for a couple semesters. While grading isn't the same as teaching experience, it does reveals so much of what is in the students' minds (perhaps prior to taking the course even), as well as reveal what the student has not been able to retain.
As a graduate student at the University of Virginia, my first two years were spent as a Teaching Assistant (TA) where I would instruct night labs. The first year, this was Constellation Quiz and Observational Astronomy. In the former, I would introduce students (of ASTR 1210/1220) to the night sky, often by pointing out a couple easily-identifiable constellations, the north star, and talk about how to (roughly) measure altitude and azimuth. The students then work through several questions (in small groups), and at the end the TA administers a quiz on 10 objects (constellations, individual stars, or planets). In the latter, students (of ASTR 1230) work through several labs throughout the year, building up in difficulty, such that a student should be able to come away from the class knowing how to use a (personal) telescope to look at an object in the night sky.
In my second year, I helped with the Telescope Observing (TelObs) night lab, where 2 TAs and 2 telescope operators run the McCormick observatory and have 3 telescopes and a pair of binoculars for students (of ASTR 1210/1220) to look through. Students must draw with relative accuracy what they have observed and write down a description of the object (from known facts to what they observe for themselves). In my third year I was a telescope operator for the 6" and 10" telescopes. Currently I am a telescope operator for the 26" McCormick telescope.
Currently I am tutoring (through the athletic department) several students of introductory astronomy classes. Having the same students over a semester has allowed me to watch students progress throughout the year and monitor what motivates students, and what they retain. The tutoring sessions are of my own design, so I choose what to focus on based on what I think the students already know, and need to know, for the class.