The above image is an example of a schedule that your child could be sleeping by, but for us we don't really have a sleep schedule. I let him sleep as he wants and I get up when he does, to nurse him.
Our older two children were formula fed and slept all night at 3 months old. No magic formula by any means, they just slept all night. They were sort of on a schedule where they woke up every 2 hours until 1 month old, every 3 hours until 2 months, every 4 hours until 3 months, and then after that they slept all night until 7am.
With our youngest, he's breastfed and has been since birth and he slept about 4 hours a night at 2 - 3 weeks old. Of course, I didn't like that only because I thought he was suppose to be on a schedule but that's not the case - if he's hungry, he'll wake up to nurse. He's now 7 months old, and when school is in session bedtime is between 8 - 8:30pm for all 3 kids or I try to anyway, and he wakes up around 6:30am to nurse, and he usually ends up either falling asleep for another hour after eating or just stays up until naptime.