How to get burnt stuff off bottom of pan?

You need an abrasive. Baking soda works, or something called "bartender's friend" which is great.

Also, frankly, salt. A bunch of salt and some oil will scrub up the burned bits pretty well.

If it's a stainless steel pan, try using a steel wool scrubbing pad, like SOS brand ones. You may also need to some abrasive cleaner like Comet.

Put some water and a dishwasher tablet in the pan and then “cook” it slowly for hours, making sure it doesn’t boil dry

So you've soaked it, ok. I use card keys from hotels as food scrapers. They work wonderfully!

If all else fails I just put it for a cycle in the dishwasher and it softens it and then hand wash it.

Put water in the pan and boil it -- that usually frees the burnt-on crap.

Put dishwasher detergent in and let it soak.

Always start gentle and then increase.

@samueltyler2's idea (w/hot water) is a great first step.

If that isn't entirely successful:
If it is NOT cast iron, or ESP if it's "non-stick", they make non-scratching pads (ScotchBrite or sthg; you have to check the label, as one pad color is non-scratch and another is *not*).

On the cooking surface ? Put water in it and then a downy dryer sheet and let it set overnight . It is easy to wipe off then. If its heavy i put a few sheets in the pan

You can heat the water in the pan. Or heat it with oil. And wipe it with paper towel

Easy-Off oven cleaner? The same stuff used to rid one's driveway of oil stains?

Try soaking it with a paste of barkeepers friend and then scrubbing it

soak it in water and vinegar, baking soda also helps

Keep it on the stove, low flame/heat,.and boiling water from the kettle, enough to cover it, and as it heats use a wooden spoon to loosen the burns

It’s always best to clean immediately.

I always use nonstick pans so I don't have to deal with that. Totally worth the investment, and nowadays some nonstick pans are even made of materials that doesn't get scratched by metals, which is amazing although usually too expensive

I have a metal spatula I use for pretty much everything in the kitchen, including that.