First, if you live in an apt and your neighbor has fleas, you're screwed.
I went for the overkill approach when my pet got fleas.
I put a flea collar on him, gave him a flea bath, then laid on the flea powder. Then I bombed the house.
The next day, another bath, more powder.
A few days later, bombed the house again, another bath.
By this time I saw no more fleas, but a few days later I bombed the house again, another bath. Just to be sure.
I put powder on him daily, and kept the collar on for a few months.
I haven't had a flea problem since. The fleas that escaped probably still pass that story on to their kids.