If you're looking for cheap (<$5k) cars, avoid any used car dealers. They're predatory at worst, overpriced at best.
Craigslist is the way to go. I actually just bought a car this week on Craigslist. My method for Craigslist are basically this:
Figure out exactly what you want. This doesn't mean necessarily something specific (I want a green 2006 Honda Civic with exactly 122,513 miles on it for $4200.15) but some general parameters. Maximum miles, minimum year, max price, list of makes and/or models. Make it all into once search, and save that link. Here's mine I was using:
https://chicago.craigslist.org/search/cto?query=corolla%7Cyaris%7Cprius%7C%22honda+fit%22%7Ccivic%7Cscion%7Caccent%7Cspectra%7Cforte%7Cmatrix%7Cvibe%7Csentra%7Chybrid%7Celantra&sort=date&min_price=500&max_price=3000&min_auto_year=2003&max_auto_miles=140000&auto_transmission=2Check the link every day, ideally multiple times a day if you can. You'll pretty quickly get a good idea of what's out there and what's a deal and what's not.
Ignore any listings that are sparse on details. Ignore any listing with super crappy photos, or no photos, unless it otherwise has a good lengthy description.
When you find something good, call (not text, not email unless there's no number) as soon as humanly possible. Ideally within a few hours of listing. If you don't get an answer, leave a voicemail, and text or email immediately after as well. When you call, be able to look at it that day (not necessarily that instant); otherwise don't bother.
Research the model. Know what flaws they tend to have, big or small (not just big scary engine/transmission troubles but common places they rust, certain things that tend to break or leak, etc.). Know what expensive maintenance might not have been done (timing belt, etc).
Bring the asking price in cash when you look at it. Have a plan to drive away with it that day, even if it's a bit silly (I drove our other car there alone, drove the "new" car home, and then Uber'd back to grab our other car).
Slowly look over the car. Make observations and ask questions, but don't hand-wave away issues or talk too much. Let them talk about the problems. Pop the hood and check the fluids, even if you're not a car person and don't know what you're looking for 100%. If fluids look old or low, comment on that.
When you take it for a test drive, accelerate up to highway speeds. Do this both slowly and quickly. Note how smoothly (or not) the transmission shifts through each gear. Test the brakes. Brake HARD at least once. Take your hands off the steering wheel (safely) while driving but also slowing down at least once, to note if it pulls to one side in either situation. Note any excess vibration in any circumstances. Mostly drive with the windows open, so you can hear any potential weirdness. Then roll them up and blast the AC for the rest of the drive to make sure it won't quit on you (I got bit my this once and ended up with a bad AC compressor). Test the radio. Press all the buttons. Test all the features. If there's a sunroof, look for signs of leaks.
After the test drive, check all the headlights/turn signals/bulbs, etc. If a bulb is out, check to make sure it's just a dead bulb and the socket isn't damaged (not always easy to eyeball but sometimes it sure is).
If the ad said "FIRM", then hand them the money and sign the title.
If it said "OBO" or specifically said flexible, mention that (again, let them talk). Say something like "The listing said $xxxx, right?" acting maybe a little unsure. You can probably get at least a few hundred off here, especially if there are legitimate (minor) issues with the car, or it was slightly overpriced in the first place.
Drive the car home, don't turn your celebratory music on until you're halfway and have driven with the windows down as a bit of a sanity check.