If you have super-light surface scuffs that you can't see in all light and you can't catch with your nail, you might get away with a hand-friendly swirl remover. Expect to spend a lot of time and have sore arms, lol. Most likely, though, you will need the assistance of a machine.
Ive attempted at a few techniques I "learned" from online videos with a DA. The best tip I can give; use the least abrasive method possible. It requires a lot of trial/error; different pads/chemicals. Some scratches buff out pretty easily, and the ones that don't can easily cause additional, lighter scratches in the hands of an inexperienced detailer
. I did end up with a line if Optimum products and would recommend giving them a shot.
But unless you truly know what you're doing, it's going to cost more to find out what works for you/your car than to just have it professionally buffed. A decent DA alone is over $100, and you'll still need a multitude of pads/chemicals. Around here we have professionals who give a solid polishing for under $150.
They also detail your car