You simply need to click on them once you are in your Medal Box.
- Use "X" to pull up the menu
- Click "Bag"
- Move to your "Key Items" Case
- Scroll down to "Medal Box" and press "A"
- Press "A" again
- Scroll through the pages until you find a Hint Medal (They are silver and have a question mark on them)
- Click on it and the text that appears on the top screen below the image of the Medal is the hint
In case you're not certain that the text which appears is actually the hint, I went and looked at a hint medal I had, which said:
Use a convenient vending machine when you get thirsty.
I went and bought a couple Lemonades, then talked to Mr. Medal in the Castelia City Pokécenter, who awarded me with the "Vending Virtuoso" Medal, and the text now reads
A medal for thirsty trainers who bought 10 or more drinks at vending machines.
List of Medals