I'm a little proud to say the I taught my rex kittens that curtain climbing was not the IN thing to do before they left my home at 4 months of age.
As they had free run of the house growing up, they would discover curtains and swinging. I used a combo of a sharp "NO" and clap my hands when they started or got the water bottle out. If doing it consistantly and catching them each time with either method they soon learned there was other things much better to get into.
If you don't have one, get a nice tall tree house climber for your kitten. The water bottle works wonders! Our 6 month old kitten found that out with the Christmas tree - about 6 times of being hit with water, she no longer has any interest in climbing the tree or playing with the decorations
I've had compliments from those owners of my kittens of "your kittens are so well trained, they don't even climb the curtains like all the others I've had in the past - how did you train them so well?" I believe in stopping bad habits before they start (curtains and furniture scratching are big no-no's).