I am probably going to get slammed by some other responders for this, but first let me say:
** I totally understand what you are going through. Being so exhausted you want to cry and being barely functional the next day. **
We did the Ferber method of crying it out. That day we started it, well before bed time, I told my son that there would be no more milk at night and that night was sleeping. I reminded him again of this as we started our nighttime sleep.
Then, when it came to bed time, I said goodnight and I would see him in the morning. He was used to falling asleep on me in the rocking chair... "I" was his security blanket and I could not live like that. It was one thing when he did just at bedtime, but it got so that it was 2 or 3 or 4 times at night, when he'd wake up and then want me to hold him again so he could go back to sleep.
Anyway, I put him in bed (made sure I kept him up a little later than usual so he was a bit extra tired). Then, if he cried, I let him, following this pattern:
* Let him cry for 5 min, then checked in on him. Told him, I love you, you're safe, it's time for sleep. And left the room. Do not engage in conversation, etc.
* Then, let him cry for 7 min, then check in on him. Told him, I love you, you're safe, it's time for sleep. And left the room. Do not engage in conversation, etc.
* Then let him cry for 10 min, then repeated the check, "I love you, you're safe, it's time to sleep" bit. Do not engage.
* If needed, go back in at 10 min intervals to repeat the "I love you, it's time to sleep." Do not engage.
The KEY part of this, though, is that if the child is calming down (volume of cries is decreasing, or cries are becoming more infrequent, or there are now pauses between cries where there were not before)--- Do Not Go In to check. Just let the child be.
It broke my heart and I cried, but I really needed him to learn to fall asleep on his own. I am a much better parent, and person when I have good, uninterrupted sleep.
I will also say that you may need to repeat this process, particularly after an illness.
And last note: don't do the crying out method when the child is sick.