Depends on when it flowers. If it's a springtime one, eg Montana, cut it back when it's finished flowering. Ditto the winter varieties. If it's a summer one then it's usually February/March when you cut it all back to about 12 inches.

There are three pruning regimes for clematis, depending on variety -the species clematis don't need any cutting back at all, (such as montana) unless you want to keep their size in check, in which case, prune immediately after flowering for spring flowering ones.

The large flowered hybrids are pruned (or not) according to when they flower; those which flower on growth made the same year are hard pruned by mid February, down to about 2 buds or 10 inches from the ground. These all fall into the viticella or jackmanii group, flowering from late June or July until the first frosts.

The spring and summer flowering hybrids, such as Niobe, which produce large flowers late spring, then flower again late summer with smaller flowers, just need a bit of a tidy up, or can be left alone to do their thing. They're quite difficult to 'tidy up' in between one flowering session and the next - you may inadvertently remove growth which would have flowered later in the year, and if you cut before the first flowering, you'll remove flowering wood and won't get the early, larger flowers.

The early flowering ones like Nelly Moser don't need any pruning - they flower on wood produced the previous year, so if you cut that down, you won't get any flowers next year.

It helps if you know the variety - that will tell you which group your clematis belongs to.
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If you don't know t variety and can't work out the group then the best guide is to prune after flowering.

No, you don't, Snoop, but if you need to eventually because its getting too big or spreading too far, make sure you do it immediately after flowering.