I only took impressions twice. The first time was the day I got braces put on and the second was the day I got my braces taken off.
I didn't gag, but was actively focused on trying not to.
The tray of alginate is put into your mouth, in my case one jaw at a time, and it feels gooey. The orthodontic assistant will time how long it stays in and feel the alginate to determine when it's solid. Then it gets pulled out, you wipe the excess off your lips and repeat.