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.
One of the biggest mistakes parents make, no matter what method they use, is being inconsistent. At some point your little one will cry for you in the middle of the night, even if you think you've all made it over the sleep-training hump. Go to his cribside to check on him and make sure all is well—just be sure not to restart an old sleep crutch during this check. After that, try comforting him from outside the door, if you can. If you regress due to illness or travel, get back on the training wagon as soon as possible. Otherwise you risk sabotaging the weeks of hard work you've already put in.
Thank you for your comment! We agree, and we think most parents do, that cry-it-out is a last resort, and we always recommend trying a gentle sleep coaching method first. That said, the research on cry-it-out is that, done correctly and not as a replacement for parenting your baby, it is not harmful, and can indeed be beneficial when you consider the damage that lack of sleep can do to a baby’s overall health and well-being. We have an article with further information about our philosophy on cry-it-out here: https://www.babysleepsite.com/sleep-training/cry-it-out-age/
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.
This is considered a ‘cry’ method of sleep training. This technique entails allowing your baby to cry while checking on him at intervals. The goal here is to reassure him every so often that you are nearby and to reassure yourself that he is okay. When you go to check on your baby, you are not “supposed” to pick him up nor engage him much, but simply reassure him using your voice and a loving pat for 2-3 minutes, tops (watch the clock!). With this sleep training method, the goal is NOT to help baby fall asleep – that is what he is learning to do on his own! Instead, the idea is that he falls asleep on his own, in the same “environment” in which he will awaken periodically throughout the night. The knowledge of how to fall asleep unassisted at bedtime will pave the way for him/her to go BACK to sleep throughout the night. Over time, you gradually increase the amount of time between your ‘checks’. See a more detailed step-by-step explanation of this method here: The Ferber Method