The answer isn't concrete
There is no hard and fast answer to the question, "When will my baby sleep through the night?" And each baby is so different. My son started sleeping through the night (I'm talking a good 11 hours) when he was around eight months. My daughter woke every night for the first year of her life. Then, like a switch went off on her first birthday she started sleeping through the night.
However, there are patterns that you can look forward to. At around two months of age your baby will probably be able to go at least four hours without waking, meaning you may only need to wake to feed him once or twice a night.
At around four months, most babies can go eight hours without waking to feed and by six months, babies, especially ones that have started eating solids, can sleep up to 10 hours without waking to be fed.
There are other factors, of course, that may contribute to your baby waking in the night. He may wake looking for your comfort, or a wet diaper may have disturbed his slumber. When you go to him in the night, try to determine the cause for his cry before disrupting him too much.
Continue to set the stage for sleep by keeping lights low if you have to change his diaper or bring him out of the bassinet to feed. Sing softly to soothe him back down as you finish up his feeding or diaper change. If baby is simply looking for some snuggle time with mom, offer it to him, of course, but try not to prolong your stay as baby may look forward to these night-time visits and start waking to get more midnight mama time.
Create a sleep pattern
To encourage baby to sleep through the night, create a sleep-time routine that he will begin to recognize. Give him a warm bath, read a book or sing to him and then swaddle him and lay him down in his bassinet with a soft music and light toy (that's out of reach!) to lull him to sleep.