I knew teenagers driving cars was a thing in the US but I assumed they were driving their parents' cars. How do they afford it? I still don't own a car because I don't need one where I live.

Same way they can afford anything else - Either they work to earn money pay for it or their parents pay for it.

My first car was $500, my second was $200. You buy used and old. Myself and most of my friends were willing to work on them ourselves for minor repairs that were needed. Lots of kids got hand me downs as their parents bought themselves a new car. There were lots of cheap clunkers to be had back in the day. No idea what the used market looks like these days though…