If you are the driver of a friends car involved in an accident are you covered under your insurance or the owners insurance?

depends on the company and the details of the accident. most commonly the owner of the vehicles' insurance will pay the claim and then subrogate (recover money paid out) against the drivers insurance company.

for example, let's say you have state farm and i have allstate. you are borrowing my car and get into an at fault accident that cause $10,000 in damages. allstate will go ahead and pay the $10,000 to the other party. once that is done allstate will basically send a bill to state farm for the $10,000 they paid out.