IME, pretty much any clematis can be rejuvenated or cleaned up with a good, thorough pruning :-) However, if your vines haven't been attended to recently, it is difficult to know where to start. If you can, attempt to unwind the vines and begin cutting back from the top - this is often easier said than done! If a huge tangled mess, then start from the base upwards - trace the stems emerging from the ground and follow them upwards until you see other stems or shoots emerging. The shoots will be held in the axils of previous vining leaves and if low on the plant, may only just becoming visible. I'd count up to the third set of these from the base and cut back at this point.

This may seem excessively harsh, but it typically will not phase the vine and promote some vigorous new growth. Just avoid cutting back too severely into any thick woody stems. In these cases, you may want to take it back somewhat higher up the vine. If it is a type I clematis, you will lose the blooms for this season. Type II and III will be unaffected as to blooming except to delay the start of the II's slightly. Hard pruned II's should start blooming in our area around late May/early June and the III's by midJune or July. I'd fertilize soon after pruning and provide regular care going forward. And to avoid this situation in the future, do an annual pruning about this time (or slightly earlier) on II's and III's each year. Type I's do not need routine pruning and I'd avoid it unless to control size or to clean up a wildly overgrown plant.

I agree with Pam. The rules are guidelines only. Depending on the length of your growing season most of the type IIs can easily be treated as type IIIs and you wouldn't know the difference except when the clematis would bloom (later in the season than if they had been treated as type IIs vs. type IIIs. Only the type Is might be affected although the shortlived type I alpinas I have grown will even rebloom later in the season again if they are pruned as type IIIs. The only type Is that you will miss the bloom period for will be the montanas if they are treated as type IIIs.