When does it bloom? That will help tell when to prune it. If it blooms in May in zone 6, then it's an early large-flowered and should be lightly pruned after blooming since it sets flower buds the season previous as well as on new growth. If it blooms in the summer, it forms flower buds on new growth, so to have flowers on the whole plant rather than just at the branch ends/tops, you want to prune over the winter any time after hard freezes have put the garden to sleep for the winter and before they are leafed out in spring.

If you prune it "wrong" or skip a year, it won't hurt the plant, but it may delay or reduce flowers for the season.

I honestly can't remember. I was gone last summer for 5 days every week. If my memory serves me correctly it blooms pretty close to when the bearded iris do around here. I was hoping someone would recognize the variety and be able to tell me.

There are too many purple large flowered clems to be sure.

Since you don't know when it bloomed, you have a choice, and neither will hurt the plant long term. If you hard prune and it's a type 2, you will delay flowering a few weeks, and if it's a type 3 it will bloom over the whole plant since it blooms on new wood and so is usually hard pruned. If you just leave it until after flowering and it's a type 2, you can lightly prune after and you may get a second bloom in late summer/fall though it depends on specific type and location, while if it's a type 3 it will bloom more at the top of the plant. Watch when it blooms this year, and then you know when to prune after this.

As BorS says, you can't tell from the photo for sure, though if you want to rummage around through Clematis on the Web, put the info you do know (leaving the rest blank) and then see which clematis it suggests. Look at the leaves, buds, flowers (remembering that blue tones don't usually photograph accurately) relying mostly on petal AKA tepal shape and size as well as the color and shape of the boss of stamens in the center, and think about plant height. Unless this came from a specialty shop, it is probably one of the more common clematis, and C on the W is full of plants rarely (if ever) seen on the US market, so you may just find it frustrating.

You could also try poking around at the base of the plant since whoever planted it may have tucked the tag in somewhere and you can get the name that way.