No one’s mentioned the Ferber method yet, it’s what got my daughter to start falling asleep on her own and do full nights at 5 months old. Took about 4 nights.
I do remember that quite sharp 'parental pain' (it's hard to describe, it's like an intrinsic 'hunger to help') of knowing that we have to get through the next X minutes of baby crying without going in there. It's good to have a supportive partner so you can both keep each other in check (or to put it how I'd prefer: "well, we're both bad parents if this doesn't work, it's not just me").
We did soften it somewhat by setting the maximum interval at 7 minutes (we couldn't stand longer than that). It might have slightly reduced how quickly the method works (although we started to really see great progress 4 days in which is in line with the book).v