May be common knowledge for some, but I thought of this on my own. I also made a few mistakes along the way, which I will point out.
1. You will need two accounts, one with chars on horde side, one on alliance side. Move a character from each account to a goblin AH. One char must be horde, the other alliance. Don't laugh, but I made the mistake of selling alliance -> alliance just different accounts once :P)
2. Before you start your moving do /who Stranglethorn Vale, /who Winterspring and /who Tanaris. If you see any characters below level 10 in any of the areas, BE WARY. There are people who have an alt camped at an AH with a clicker addon (no idea of the exact addon name) set to catch people just like youBest to leave the moving for some other time.
3. With character A put the stack of stuff in the "Post auction" tab, set a price but don't start the auction. Make sure to put in a bid as well as a buyout.
4. With character B open the AH and type the name of the item you are about to move (eg Fel Lotus) - this is all to save you precious seconds.
5. Move to char A, click "Post auction", then quickly alt + tab to char B and hit "Search", select the item and hit "Buyout".
If done correctly, you should have the stuff on the char you wish.
Regarding setting buyout price:
1. If you put a high buyout you will lose gold due to the high % taken by those greedy goblins.
2. If you set a low buyout, you risk the stuff getting intercepted. As far as I know, the addons used to do this work by being to highlight/prompt you to buy any item which is at most X times what the vendor pays for it. The risk is of course nonexistant (I think) for enchanting mats, for example, which have no vendor value AFAIK.
The whole transaction is best done with both WoW instances in windowed mode and the windows made smaller so that you can see the full window of each instance at the same time. This makes for faster alt-tabbing than if you were to have both sessions in full screen. I assume a dual monitor setup would be best but I don't have that so I can't say.
Hope this helps at least someone.