Before you begin this sidequest, there are a few things you must do. First, you will need to be Adult Link. No part of the trading sequence is done as a child. Next, you will need Epona, as you will be transporting some items that will expire after a time limit. You will also need to unfreeze King Zora using blue fire.
While no part of the sequence is done as a child, there are two things you can do as a child to prepare for the quest. The first is to learn the Sun's Song, as you will have to wait for extended times at two parts in this quest. The second is to plant a magic bean seed at the entrance of Dodongo's Cavern, as you will be racing up Death Mountain near the end of this quest.
Finally, keep in mind that during sections where you must race against a time limit, you must not use any warp songs. This will bring the timer to zero and you will have to start that section of the quest over.