A very stuck oil plug

Metal expands when it heats, so warming an engine isn't a good way to free up the plug, although it's good to have warm oil when you change it as it flows more freely. First, get some penetrating spray like WD40 and spray it on. Then spray more on 20 minutes later. Then spray more on 20 minutes after that and try the nut again, repeated sprays and giving it time to soak in can work wonders. Spraying and leaving it overnight isn't a bad idea.

Next, get a longer lever. A breaker bar or something similar will give you lots of torque on the plug. If you don't have one use a "cheater", which is a length of pipe that fits on the end of your wrench. Make sure you are getting a good grip on the plug and not rounding it off.

Once you get it off make sure you torque it down to spec, the reason you're having problems could be it was over-tightened in the first place. 14 foot-pounds seems to be a common number but check your service manual to make sure.

Once you free it and it starts to move you could then heat up the engine to get the oil warm, then stop it and remove the plug fully to drain.

Oil change tip - how to loosen a stuck oil pan drain plug / bolt: https://www.youtube.com/watch?v=UwqA1vifRjI

This guy shows exactly what you are looking for, 'IF' the problem is not a rounded off bolt.

If the bolt has been rounded off by repeated attempts to get it out, there are several options available to you. I don't have all the terminology, but this fellow explains and demonstrates several methods of removing rounded bolts: https://www.youtube.com/watch?v=ix1-NVOC83w

A great explanation of extractor sockets and tool quality vs performance: https://www.youtube.com/watch?v=_EfLTszAr7w

When you get it out, move your head real quick. I'll never forget my first oil change. LOL I don't know which was more humiliating; the fact that it happened or the merciless ribbing I endured afterwards. :)