Late February and early March is the best time for Pruning Clematis to ensure it produces lovely flowers year after year. Clematis prune can seem a bit complicated, but not really. Group 1 Clematis do not prune at all, and group 1 flower early in the year. Group 2 is a light prune, and Group 3 a hard prune. To check which you have there is detailed information on the Clematis pages to help identify the group to which a clematis belongs if you have no labels or information. If all fails and you have no idea, Group 2 usually flower in mid summer and Group 3 later in summer which is not true of every type of clematis but it can be the best guess.
All the books and magazines say "prune to an axial bud" so to know what to look for are two images below. At this time of year on some Clematis the axial bud will be easy to spot, as in the first image, on others is can be quite small and you need to look carefully.