I hate righty-tighty lefty-loosy. Depending on whether you're looking at the top or bottom of the screw, you can see movement to the right or the left. I hate whoever came up with it, and I wish I had been taught the right hand method. It works exactly the same as the electromagnetic right hand rule: an example of the right hand rule as it relates to a screw thread
Basically, you take your right hand, stick your thumb out, and curl your fingers like you're grabbing a broom handle. Point your thumb in the direction you want the screw to move to. Want to screw something in? Point your thumb towards the thing. Want to unscrew? Point your thumb away from the object the screw is currently in. Then, just look at the way your fingers are pointing! If it helps, squeeze your fingers into a fist and see which way they move. Alternatively, bend your wrist in, and observe which way your fingers are moving. Works every time.
It sounds complicated, but there are plenty of people who are unable to intuitively differentiate from right and left the way they can differentiate up and down. I am one of those people. Thanks to this method, I've been able to develop the muscle memory/intuition to know which way to turn a screw.
It's important to note that this only works for screws that are "right hand threaded." If the screw is only getting tighter when you're using this method, then it's likely reverse threaded, or left hand threaded. If that's the case, just use your left hand instead of your right hand.