Just started, so my question is very basic. I got Coopers Lager Kit, did everything by instructions, temperature has been stable at 22-24C but gravity doesn't go down. OG was 1.039, dropped to 1.020 on the 4th day and stays at that level for several days (today is 10th day of fermenting with very little bubbling). Tastes very bitter. What is wrong? Should I just bottle?
1.020 is quite a high final gravity. It sounds like your fermentation is stuck. I would swirl the fermenter to resuspend the yeast (without introducing any air) and see if fermentation resumes. If that fails, then I would buy more of the same yeast that you originally pitched, if it's dry yeast rehydrate it in 90-100F water (32-38C) for 15 minutes, then add it to the fermetner. If you used liquid yeast, make a starter, and when the starter is bubbling fiercely, add it to the fermenter.
If you didn't make a starter or didn't rehydrate dry yeast, high final gravities are frequently what you get.
Some kits are intended to have higher final gravities, but you got less than 50% apparent attenuation. You should expect at least 60% and probably more like 70%.
I would be more worried about the bitter taste, was it bitter or acid as in vinegar? As Korz already said it could be a stuck fermentation. I think the yeast packets in the beer kits are not under ideal conditions most of the time and stuck fermentations should not be very uncommon. Swirl or re-pitch in that case. But an infection could also leave your beer in that state, you should smell and taste it, just make sure to use sanitized equipment to taste it or you could end worse than what you started with :D.