How do I locate military records from 1944?

I recently ran across a journal written by my grandfather about his experience in WWII. I would love to look him up along with some of his closest friends. He always wanted to do that but he passed away before the computer age. How in the world would I go about this?? I did manage to find an obituary on one such friend. Some of the names are very common. Does the Army have such a site?? He also played ball for one year before the war with the St. Louis Browns. Would there be anything out there on that?? Thanks!!

HALEN