Someone can offer you a swap by clicking the "Offer a Swap Deal" link on your auction's page. You will be notified by email when that happens.
Login to the members area and click the "Selling" icon on the left, (the one with the red arrow pointing up.)
You'll see your auction listed, and under the "Max Bid" heading, you'll see a text link that says "Swap Offer From <username>", <username> being the registered user who offered you the swap.
Click that link. You will see their description of what they are offering in trade, and two buttons below: "Accept Swap" or "Reject Swap"
If you click the accept button, that person "won" the auction and the auction will close automatically. If you click the reject button, they will be notified by email that you did not accept their offer and your auction will stay up until it either expires or you accept something.
(By the way, the pics of your plants weren't being put up on the the OrchidTalk lobby page because they were links on another site, and I forgot to account for that in the code. This should be fixed now...)
Good luck on your trades!