How do I fix this HORRIBLE drywall patch?
It's not as bad as you think.  Someone just skipped the last step in drywall repair, and proceeded to paint.  The wonderful thing about drywall is that when you screw up, you can generally fix it without starting over.
As another poster suggested, you just need to feather everything out, and sand.  I'm not a pro drywaller, but I'd think you could get away with just one application of mud+sanding.
Check out this guy on youtube, who gives pretty good advice on drywalling techniques.  I'd highly recommend youtube for something like this, as it's hard to describe drywall techniques in words or even pictures.
https://www.youtube.com/watch?v=BUcT5LHmA7w