How do you drop items?

There are two ways to drop items; you can put them in the hotbar and press q, or you can also open your inventory, click on them, and then press q; because the item you just grabbed is now in your character's hands, it'll be dropped.

But, as of the latest patch, the developers claim to have made the following change:

All player drops are persistent now. So if you accidentally throw your diamond drill down a mineshaft, you don’t have to suicide trying to get it back before it disappears.

So, dropping items with q won't actually get rid of them; they'll sit around for eternity, just waiting for you. There's a far better way. On the inventory screen, there's a slot with a big "SEND TO TRASH" label on it; put items into that slot, and after a moment, they're gone. Forever. No longer cluttering anything up.

Can't try it out right now (game needs an update don't use my laptop that often), will edit the answer in a bit.

I am pretty sure that you can drag an item from the inventory (which activates it) and then drop it pressing Q.