Well.............first note that this was a thread I started last year. I don't really have things organized yet for this year. But what I have always done is do the actual trading in the spring, as weather after digging can be really chancy for shipping tubers safely.
On another site that I frequent, everyone posts a list of the tubers that they expect to have available for trading (after they dig and see what they have), then participants contact each other (tree-mail here would be best) with wish lists. Ideally everyone's tubers last through the storage season, but if not then adjustments are made in the spring.
Last year, I turned my ATP plant list into my list of available tubers (I had a lot and was selling as well as trading) It worked well because pics and info became part of the list, and its easy to edit as the number of available tubers decreases. I then posted this thread here and posted a thread in the ATP classifieds which reaches more people than just the few of us that frequent the dahlia forum. However, what might work better for us as a group is to start a new thread here "Available for trade spring 2016", and everyone could post their lists there, and/or if they want to use the ATP plant lists, post a link to their page.
I prefer to ship using priority mail. The small boxes ship for about $6, and can hold 6-10 tubers depending on the size of the tubers, the medium boxes are 12.65 (?) and can hold up to 25 or so. If its only 1-2 tubers then you can sometimes get away with using padded envelopes, but some tubers are just to fat for those. Last year I put 1-3 tubers in ziplocks with vermiculite, labeled both the tubers themselves and the baggies, and everything arrived safely.
I won't be digging till closer to the end of October, so probably won't have my list together until early November. But if you are ready to go then you could go ahead and start the 2016 trading thread.