Aiden started to hold his own head up at a month and it is just getting stronger and stronger each day
My son started really holding his head up well at 2 months, but that is early. Between 3-4 months is typical, I believe.
It's different for each baby. You can get this cool book at Walmart called Your Baby Week-By-Week. It'll tell you milestones your baby may be hitting weekly.
Holding their head up straight, while laying on their bellies, will happen closer to 3 months, I think. It's hard to remember.