Once you enter a shop and select a menu, you'll be shown different items to choose. To buy one, simple highlight it with the directional buttons and press (X).
You can also sell items. Each items is worth half of its original price when sold.
When shopping for items, there will be an equals sign by each character. However, when you shop for magic, armor, and weapons, an icon will appear by the character to show if it will help the character, keep it at the same level, or if the character can't use it.