The person creating the auction chooses how long it will run for. They will pick the end date and time (in their local timezone) when it will end. It will last for a minimum of 2 days and a maximum of 28. Once the auction has ended the buyer has 7 days to finalize the payment before the transfer is completed at the following server save.
"On the next page you can select the starting price for your character's auction and choose at which day and time your auction should end. Note that your local time is displayed there. The end point of the auction has to lie between 2 and 28 days from the auction set-up on."
"Once the auction has ended and you hold the highest bid, the price will be paid automatically if you have sufficient funds. The Tibia Coins previously reserved will be made available for this purpose. If you lack the necessary funds, you have 7 days to pay the selling price. When paid, the character will appear in your character list after the next server save."