How do you go about crown dipping and cresting carbon arrows?

You may want to consider wraps from onstringer. Consistent, looks awesome, very efficient.
http://www.onestringer.com/

It's a wise ideal to plug the nock end of the arrow shaft before dipping. Small corks work well. Aside from that, there's no difference between capping and cresting wood shafts, or those made from aluminum or carbon.

I do it the same way as I do for my alums.  I use a dip tube and dip each shaft with the paint color I want to use, let dry and dip again.  When the crown dip is completely dry, I proceed with the cresting using a cresting machine.  When the cresting is dry I usually spray with a clear protective top coat.  
I realize that this is very general, so if you have specific questions, please post or PM me and I'll try to assist.

Claudia

Is there a specific paint I need to use or can something readily available be used?

www.battledrumwraps.com   Easy to remove if fletch need repair and easy to put on...check them out.

Bear Heart,
I personally like to use Bohning paints, but there are others that will also work.  Go over to the 3R or Kustom King websites and there will be some selections offered for your consideration.

Claudia

+1 for onestringer arrow wraps......stabow

I use a lead base paint to get the weight right and good arrow flight...

I simply mask off the crest area and spray paint with Krylon paint. Fletch with fletch tape so they can be refetched later if needed. A dap of super glue on the ends maybe but it melts into the spray paint!