Usually it takes 4-5 months.Once they start rolling over by themselves ,they will lift the head up and do the pushups or you can give the tummy time .
Tummy time helps a lot..Do it every day for few mins or as much as the baby can tolerate...I think it takes anywhere from 4-5 months to fully get the head under control..But DS was able to hold it up @ 3 months and he rolled over @ 3 months..Of course he was lil wobbly up until 4 months.. BTW, I did lot of tummy time starting his 2nd month so I think that helped him a lot..
every baby is diff, so dont worry i guess by 4 months ur LO should be able to more or less... my DD started to hold it up at 3 months, ofcourse wobbly, and now is able to do the pushups with head raised when she is nearing 4 months...
My baby had her head control around 2.5 months... As Sudha said... Tummy time does help in head control.