If your clematis has already become a mess of dense growth, it may be possible to prune out congested growth, but often the best solution is to radically hard prune all the stems back to about 10 cm from the ground. Do this in early summer after flowering, and feed, mulch and water well, and the clematis should flower again next spring.
Hard pruning like this should not be repeated more than every 3-4 years. Also, very old, mature specimens may not respond well to hard pruning, particularly Clematis montana.