There is 3 basic groups of pruning for Clematis you only need to prune if the plant has taken over its growing space.
Group 1 the species early flowering types like Clematis montana, C. macropetala and C. alpina
This group flower on growth produced the previous year and, if needed, are just given a light pruning to remove spent flowers immediately after flowering.
Old, woody plants can be pruned very hard - down to 60cm (2 ft) if necessary, preferably to just above some strong, healthy growth - after flowering to remove lots of the old, non-flowering growth. Plants may take a year or so to fully recover and start flowering properly again.
Group 2 Large-flowered hybrids which start flowering in May/June
These varieties can be cut back fairly hard - say to between 90cm to 1.2m (3-4ft) high - to just above a fat pair of buds/single bud; the former is better.
Start pruning at the top of the plant and work your way down.
Group 3 Large-flowered hybrids which start flowering in June/July, and C. texensis, C. tangutica and C. orientalis types
These can be cut back very hard - say to 23cm to 45cm (9-18inches) high - again just above a pair of buds/single bud - removing nearly all of the previous year's growth.
Start pruning at the bottom of the plant.
Pruning of Group 2 and 3 varieties is carried out at the end of February/early March.
Even though some years encourage a lot of early growth on clematis, don't be tempted to prune Group 2 and Group 3 varieties any earlier, as frosts can still kill this early growth leaving none to grow away on hard-pruned plants.
If you want to retain some tall growth on plants to retain cover of the supporting structure, you could cut down just half the shoots as described above. This will give slightly earlier but higher flowers on the un-pruned growth. The pruned shoots will flower a little later and produce flowers lower down the plant. This gives a better and slightly longer display.
As with any plants, pruning should be followed by a good feed with a granular fertiliser. Rose food is excellent for this.