Once there is at least one trade offer on each side, your tradepost is ready to go. Your trades will execute around the clock. You don’t have to be online. Items that were bought by tradepost end up in the Storage Room and can be picked up at any time.

Where does the money come from to buy the stuff? Do I pay on pickup - if so, the seller has already been paid? Does the post check money made from sales and deduct from that when somebody sells an item to the post?

The guild tradepost does not use currency or "money". It's a barter.