the inventory is in the bottom left, the equipment in the top right, and the map in the left.
You can drag items to and from any control (well, not from the map), and it will either replace the old items with the new, or unequip/drop the item as appropriate!
edit - ghostanime suggested that I make ctrl-click do the equipping and unequipping, so I did, thanks!

(the gui will probably change, but i'm looking for comments on that, too, if anyone could..)
Why don't you have it say which hand is your "main hand." I'm right handed, I don't carry things in my right hand and say, "I like carrying things in my main hand!" I don't mean to nit-pick but it just struck me as strange.
You could probably make the map larger to remove some of that empty space, too.
Good luck!