I didn't do CC (or CIO) either, but my advice would be:
Have a routine. No, a routine does not mean you can't be AP. Children thrive on routines. Choose a wake time (probably between 6am and 8am) and stick to it every day - treat any waking before that time as night time. Stick to a consistent bedtime.
Regular naps - usually a 2-3-4 schedule works, e.g. 1st nap 2 hours after waking, second (longer) nap 3 hours after waking, bedtime 4 hours after waking. Initially it doesn't matter how you get them/keep them asleep for naps - sling, swing, car. Try to do different things though.
Bedtime routine. Short, sweet, consistent. Separate feeding and bedtime - so bath, milk, brush teeth, story/song, bed. Not feeding to sleep is vital if you have a baby that wakes to feed every time they go through a light sleep phase at night.
Introduce a comforter. Use it at every feed, cuddle, bedtime. Try a dummy.
Put your baby to bed. Pat them, stroke them, sing to them. If they get up, lie them back down. If they get really upset, pick them up and cuddle but put them down again as soon as they calm down. Yes, it will take a while the first few night. Yes, you have to stay consistent. Gradually you can reduce the amount of patting or stroking.