The following is a general manual; it lists controls and basic gameplay ideas. For more detailed explanations of game elements, check out the sub-manuals:
In the field: (The field is anywhere besides the world map and battle.)
On the world map:
Unlike FF games, you can do several transactions while still in the same shop screen. Here's how:
You can see the name and description of the item you wish to buy/sell on the bottom of the screen. Pressing Y will toggle the description with the stats of the item. Press right and left to add or subtract that item from the total at the right. For example, on the picture above, you're buying 2 Mithril Meshes, 1 Holy Rod, and 1 Mithril Gloves for a total of 76000 gold. The "OWNED" at the bottom right tells you how many of that item you already have. You can never own more than 15 of any item. You can't buy more than you can afford, by the way, so don't worry about that. When you're done, press A to finish the transaction.
At the top right you can see how much gold (money) you have.
The arrows by each character tell how the new item rates with the one they have on. A red down arrow means the new item is weaker than the equipped one; a green up arrow means it's better; and a gray sideways arrow means it's equal. The green "E" means the character's already equipped with that item. Note that the criteria for "better" and "weaker" might not be the same as you would choose; some armor has better elemental protection, for example. For an explanation of stats and elementals, see the Menu Explanations, under Stats Menu and Items Menu.
The "TOTAL" tells you how much money you will have spent (or gained, if you're selling) when you're done.