How can I paint kitchen cabinet hinges?
Just to stop the ugliness, I would just get a can of Rust-Oleum gloss enamel (black, white, whatever), then remove the hinges from the cabinets. 

Clean them thoroughly, and if there's any existing lacquer or hardcoat, try roughing them up with a bit of steel wool. If you can completely disassemble each hinge, that would be ideal; otherwise, work a small amount of silicone lube or grease into the action, to help keep the paint out of the hinge itself (keep the outer surfaces clean, though). 

Then, simply give them a couple good coats of the enamel spray; each coat should cover well, but don't go too thick or you'll get runs, drips, etc, as well as having paint over the tops of the moving parts (which will then crack the first time you move the hinge). Let dry, flip and repeat. When both sides are done, reassemble and reinstall the hinges. The enamel should cure into a nice hard shell that should last you until you can spend the money to replace the hardware, or redo the whole kitchen.