Saitama mentioned that he got this strong through daily training, which consisted of 100 push-ups, 100 sit-ups and 100 squats along with running 10 km every single day. Also, he ate three meals a day, but only a banana as breakfast and also didn't use the AC, to strengthen his mental resistance.

Does Saitama gets stronger?

No. It has been stated in the manga by Saitama himself that he cannot grow stronger any more and that he has hit a “strength cap" so to speak.

Does Saitama have infinite strength?

For the last time, Saitama is limitless. Goku is constantly trying to break his limits and gain more power.