Actually a rose or tomato fertilizer will produce better results than an all purpose like 10-10-10. Which kind you use is up to you and you apply it according to label directions for individual plants. I generally fertilize at the same time I prune, right around March 1.

Mulching the root zone well with compost is another good method for assuring that the vine will get the nutrients it needs for good growth and flowering.

I use RoseTone. I fertilize my roses and clematis at the same time.

You can fertilize with instant or time-release fertilizers, but another good and long-term method is to top-dress or scratch in compost to the surround area where the clematis is.

Another way might be to snip off certain vines, so that you get a bushier, fuller look.

I use dehydrated cow manure by Twin Oaks 1-1-1 formula for the past 8 years and my clematis (total of 22) are doing great... I also add a bit of new fresh soil every year like Miracle Grow and mix it with the cow manure. Using cow manure and peatmoss is also great and always add 2 inches of fresh mulch in the spring. Happy Gardening! :-)