I’ve had this problem before. It’s awful. I live in a small apartment with a cat, so my infestation was particularly bad. (As bad as it was for me, it was much, much worse for my cat. When we finally got him deflead, I pulled hundreds(!) of the little sons of bitches off of him. Tens on his face and neck alone! I felt so guilty.)
I eventually did what Judi recommended with the bug bombs. It’s not dangerous, just set one or two off in your apartment right before you leave for work one day. Make sure you leave your windows open, as well as your pantry doors and cabinet and dresser drawers so no flea gets away unscathed. Wash your couch cushions or their covers and avoid putting them back on the couch until you’re sure you have the situation under control. Wait two weeks, because that’s about how long it will take the remaining eggs to hatch, and then let another one or two bombs off. The problem will not go away immediately, but soon you’ll start to see their numbers dwindle to a small insurgence.
Also, as snowberry correctly pointed out, there will be lots of live fleas in your vacuum cleaner, and they will immediately start to breed. Make sure you change the bag frequently and dispose of it in a place that is well removed from your building, such as in the dumpster on the street.