It might be strange to think of sleeping as a skill that does not come naturally. As a new parent, you’re probably so exhausted that you pass out as soon as your head hits the pillow. Your baby, however, doesn’t have this same ability yet. Although they spend a lot of time sleeping, they need to learn when to sleep (day vs. night) and how to sleep. Until they do, they need your assistance, which is why you (as you should) help soothe them to sleep at bedtime and comfort them when they wake in the middle of the night. Sleep training is teaching your baby how to sleep without any help from you - just like you’re able to fall asleep without anyone there to help you do it.
Proponents of these sleep training methods say it's okay for your child to cry when you put him to bed and leave the room, although they don't advocate letting a baby cry indefinitely. Typically, these methods suggest putting your baby to bed when he's still awake and allowing short periods of crying punctuated by comforting (but not picking up) your child.
The biggest reason why the solutions that work for one parent don’t work for another is simple. They’re not dealing with the same baby. Some babies are heavily reliant on sleep props. Others can’t sleep in a room that’s too warm. Some may not be getting enough daytime sleep, and others might be overtired. This baby might have developed an association between feeding and falling asleep, whereas that one might be ready to drop their second daytime nap. And, of course, it could be any combination of all of the above, or the many other sleep challenges that babies might experience.
Finding the ideal bedtime can be tricky in the first few months of life. Infants who take a late afternoon nap (say, 4 to 6 p.m.) may go to bed as late as 9 or 10 p.m. A good rule of thumb is that your baby will probably sleep three to four hours after his last nap ends, but you may need to experiment, adjusting your baby’s nap and bedtime schedule to figure out what works best.
The idea behind extinction (or full extinction to differentiate it from graduated extinction) is that you want to extinguish the behaviour (crying) by not responding to it. As with the check-and-console method, go through your bedtime routine, put them in their crib awake, say good night and walk out. This is certainly the most controversial sleep-training method, and even experts disagree on what you should do next—it all depends on what stage your baby is at developmentally, as well as what works for the parents.