CC can be done when you're ready, I'd say. Many people say you have to wait until 6 months, but I did cc with DS1 at 3 months, and with DS2 at 2 months and a bit. I'm absolute rubbish at soothing babies to sleep (or maybe my sons are bad at sleeping?), so this is what works for me.
One very important warning, though: if you try it for a bit, and then give up, you can make it very hard to do later. I think you can do it for one night and then reconsider, but if you give up midway through an attempt (e.g. without the baby falling asleep), you put yourself backwards.
That being said, this is how it is done, according to Ferber. You put the baby down where you want them to sleep, when it's the right time to sleep. The baby can be sleepy, but not asleep. You talk to them and leave them be. Then you come check on them at regular, but increasing, intervals. When you check on them, you try to calm them down, you can talk to them and touch them, but don't pick them up.
The book example is to visit after 5 minutes, then 10, then 15, then continue every 15 minutes, as long as the baby is upset. The next night, you start at 10 minutes, then 15, then 20 for the rest of the session.
I did 5-7-9 minutes last night, and today I've done 7-9-11.
I find the first time can take a while. And it's a horrible feeling. But it takes less and less time each time (1 hour + last night, today it was less then 30 minutes). And I find it results in much less overall crying per day, so I don't feel too worried about the effect on my sons.