Check your local craigslist and newspaper ads for cheap cars being sold by owners. 300 is a bit unrealistic unless your looking to buy something that doesnt run and needs tons of work. If you search daily on craigslist you can find cars for as little as 1-1500 bucks on there. I bought my car of craiglist a few years ago for 1500 from an old man who could no longer drive. Its an 1997 honda accord and i absolutely love it. He was selling it for cheap since he could no longer drive, its an older model, and the air wasnt working.
It takes a lot of luck to find a car for $300 that will run for a while. Every now and then you run into a vehicle that looks like heck, has a bazillion miles on it, and has several non-essential things that do not work but the car still refuses to die. Cars like this can sometimes be picked up for next to nothing but for most $300 cars the price is just a down payment since you will be constantly fixing things to keep it running.