The previous owner did a bad patch job all over the house. The patching is a lot higher than the rest of my wall. How do I go about fixing this?
Sand them flat (or even slightly dished). Apply joint tape to any cracks (my personal preference is mesh, though you'll find lots of opinions). Apply all purpose joint compound in numerous thin coats. (Purists would have you do the mesh tape coat with a setting compound. Opinions vary, but setting+mesh is technically better.) Let dry completely between coats. Sand off high spots between coats. Eventually get to the point where you're feathering out the patch with a 12" knife. Do a final sand.
If you can handle the truth, shine a bright light sideways along the patch. That will show defects.
If you've passed the light test, prime and paint. Congratulate yourself for a job well done.
Humps on walls are much harder to fix than low spots. It's all about light and shadow. I've been doing this for 30+ years and for the last 10 years have run my own drywall repair business and specialize in these small repairs. The reason humps are the hardest is that with a low spot you just fill in the low area, but with a high spot, you have to 'float' it out, sometimes as much as 4' wide. The higher the hump, the farther you have to float it out. A minor hump will still require floating at least 16" wide, whereas a larger hump such as can sometimes be found on a drywall butt joint may require floating it 2' out on both sides for a total width of 4'.
But as the poster above mentioned, try sanding it down some first. If its been painted it often won't sand without gumming up the paper and if that happens try scraping it to remove as much height as possible Then float it out. OR, cut it out and install new rock, then float that out.
It really depends on how bad the repair really is. Some appear terrible, but if the hump isn't very high, it's fairly simple to fix. Others appear ok, but require a lot of work to float it out.