I basically use the cutting method seen here: http://www.wikihow.com/Propagate-Clematis .If you have enough time to follow that to a tee I'm sure it will work but I'm rather lazy at times and I still have had good success. Almost all of them rooted and most showed nice new growth too. Obviously your mileage may vary so following the instructions exactly may be the difference between success and failure. I did lose some over the winter but I just plant out whatever I have at the end of the season. If some died, big deal, there's plenty more cuttings to be had next year.

Keeping with my sometimes lazy gardening ways, I don't use any particular soil or mix, I just used whatever potting soil I have left or soil from my yard that was available. I try to keep them watered enough to try and keep them moist but I also can't check on them for sometimes many days at a time due to summer travel so a few may rot. This may be a big deal to some but I just overcome it via sheer numbers of cuttings. I leave them in a shaded area on my deck that gets no direct sun other than very late in the afternoon or evening. I've used clear plastic bags for the tenting and white or green plastic grocery bags and it doesn't make much of a difference. As long as they stay moist with diffuse shaded light it works for me. I also have a ton of pots laying around so I'll usually do at least 10 or 20 at a time to make up for any losses but most make it just fine.

To specifically address the cutting in the OPs photo, I would chop that single cutting into 2 or 3 pieces via the instructions I already referenced and hope for the best. I'd probably stick the very bottom piece without leaves in a pot anyway but not expect it to root and I'd just discard the top part.