communicate clearly and politely, pay up on time and be patient. understand that handling this on the organizing end is a large undertaking, especially for a popular set like Toxic, and the organizers are often community members who take their own time to do all this for little to no profit at all.
the groupbuy process (even the ones that go well) can take a while, from consolidating orders, collecting payments, adjusting from drop-outs, actually ordering, the lead time for manufacturing, shipping from the manufacturer to the GB organizer, then sorting (if it wasn't already sorted beforehand), before the organizer ships it out to you.
because of all these factors, each groupbuy can take varying durations. I've taken part in about 3 so far, albeit the first one via a proxy, and there's the Sanctuary set, which I signed up for back when Diablo 3 was still a new game (keycaps which I still have not seen to date), and there's Klaxon, which started a few months ago, and apparently is about ready to be shipped out (I think the entire thing from start till end was about 4-6 months at best from the start of ordering, but don't quote me on that). Then there's the 'flash' GBs, the DSA Retro set which was open for about 2-3 weeks before the orders were closed, and it is now in production.
Thus the simple answer is, it depends. But you should be prepared to wait for anything between 3-6 months after production (a reasonable estimate), and in certain cases, up to a year. If it matters, I think danielucf, the organizer of Toxic seems to have a good handle on things. I wouldn't worry about it being the latter.
