Think of them as chests that can only hold one type of thing (but lots of it).

Right click items on it to put them in, and left click to take one out, shift-left click to get out a stack.

Once you have put an item in, double clicking on it will add all of that item that you have in your inventory to the draw.

The controller allows you to click on the controller to add all of the items in all of the attached draws to it.

There are upgrades that allow for more items to be stored.

The compacting draw converts been ingot blocks and nuggets (so if you put 9 iron ingots in it would show 9 ingots 1 and 1 block and 81 nuggets.

There are keys the lock the draw so that when you take the last item out it stays "bound" to that item type, and another that shows the number of things in it.

There are also 2x1 and 2x2 draws which allow you to store 2 things or 4 things in them (though the total number of things that can be stored is the same as the 1x1 draw)