We did controlled crying but it was a bit much for our fraught exhausted nerves at the point we did it (after months of little sleep). My MIL came and did the first few nights, after which we carried on.
First night: bed time routine (bath, book, etc) then breast fed till drowsy, and put in her cot. Told "we love you, go to sleep" and left the room with her crying immediately.
We fled the apartment. MIL made of sterner stuff remained behind and set a timer. Listened to her crying for 2 minutes, then went up, said "shhh, go to sleep, I love you", would touch her chest to make sure she hadn't vomited and to be reassured by a physical touch and walked out again. Then did it again every 5 minutes. After 28 minutes she went down. MIL slept in our room with her that night and through the night when she woke repeated the same thing.
2nd night, same again, only took 15 minutes.
3rd night, same again, took 5 minutes.
After that we carried on- sometimes she would go down with only a few minutes crying, sometimes upwards of 10 minutes. Kept to the same routine. By the 4th day she was sleeping 12 hours through.
Now, at 2 and a half she sleeps 12-13 hours/night with another 1.5-3 hour nap in the day. She goes to sleep each night with a book and a song before bed, and doesn't cry and will sometimes muck about in bed but generally down at between 7 and 7:30 and will sleep till 7-8 in the morning.
This worked because MIL was very close to her from the start, but for #2 on the way we will definitely do the same again. If you don't have someone else who can do it for you, you just have to harden your heart to the cries and remind yourself it's for their good. I am shocked now when I look at her baby photos from 4-5 months and see the huge black circles around her eyes. She was exhausted as well and clearly wanted to sleep. Best parenting decision we made so far.