I don't understand the saying "sleeping like a baby" when parents are always talking about how little babies sleep. We've been so lucky that Mia has been sleeping 5 plus hours since she's been 3 weeks old. She now sleeps (and has been for quite some time) from 7:30pm to 4:30am sometimes she wakes up between 2 and 3am for a feeding, but not too often and that's not a big deal because I get up at 2:30am to start getting ready for work.
We told her doctor this and he said he has about 100 sets of parents that would hate us for saying that. Most babies start sleeping through the night by 6 months old some don't sleep through the night until much later. In a few cases they start sleeping through the night early like Mia.
Mia's normal bed time is 7:30 and we go through the same routine every night regardless of which one of us puts her to bed. I feed her around 7pm after that we go upstairs and change her diaper and put her pjs on. Then we lay her in her crib wide awake, turn on the mobile and wave machine. We read her 3 short books and say her prayers and leave the room. Usually she's still awake, but drowsy at this point. She falls asleep within a few minutes. Some nights it takes her a little longer to settle down, but unless she's screaming we just pop in so she knows we're still there and give her a pacifier and she's fine.
Johnson's Baby has some tips to help your baby sleep through the night.