I have metal cabinets that never look clean in my older apt. Can I repaint them myself? Help!

Depends on what the landlord says.
There going to have to approve the painting and the color.
It would be nice to see a picture.
Does it look like they have ever been painted before?

those cabinets probably got a hard enamel finish at manufacture. some got a porcelainized finish, aka fused glass. that stuff won't take paint.

if you see what looks like cracking around the hinges or spade pin lock on the door, paint won't stick.

otherwise, before trying a paint job, I'd try something like an orange cleaner followed by a rinse of clean water. kitchens have a tendecy to get an overcoat of grease and grab dust.