during the three years Saitama was training and even before, he was unemployed, so from where did he get the money to "survive" ?
Certain villains have a bounty on their heads and Saitama survived by defeating those villains. See OVA episode Road to Hero.
(Contains spoilers if you haven't seen the episode.) http://onepunchman.wikia.com/wiki/OVA_0
This is probably part of some back story we are not privy to yet. Maybe he held down some job, maybe he did favors for people and got paid. His training to become as strong as he was came as a back story, so I guess his income during that time should be too