I want to set up hotkeys, but I can't figure out how to do it. The manual says "The player can drag and drop many functions from the interface into any of the slots for easy access," but I can't drag anything. What am I doing wrong?

Despite saying "many functions from the interface" it's reasonable limited to what you can drag there.

Open your inventory and and drag one of the healing potions from backpack to the bar at the 'top-middle' of the bottom half of the interface, that will set it up as a hot keyed item (Although the slots are not numbered they use the standard top row of a keyboard using 1 for the first slot, 2 for the second slot etc).

You can also drag skills and spells into those slots; click on the key or world shaped icons on the right part of the bottom panel to bring up the relevant selection just below the hot key bar and then drag out the skill/spell you want to assign (note, not school of spells but individual spell.

If you look at this screenshot you can see that slots 1-5 contain spells and 6 through 0 contain items.
If you where to grab the prowling skill (where the skill/key-shaped button has been pressed as shown on the screenshot) and drag it to the hot key bar (say slot 6) it would replace the fatigue potion in that slot and place the item back in your backpack.

Hope that helps!

Nope, still no go.

Originally, I had not attempted hotkeying any items, I asked this question because I wanted to key spells. I followed as you instructed from the inventory screen, and it turns out I can key items just fine, but I am unable to key spells. I just now tried to key prowling, and that didn't work either. (If I try dragging from the bottom left prowling icon, he insteads try to run to that location, and dragging from directly underneath the hotkey slots results in the same nothing as my attempt to link spells.)

That's it! I had to drag it with the right mouse button. Using the left to drag just doesn't work.