I have a block, and I want to right click on it and check if the held item is a bucket of lava, and if it is, then add lava to the capacity of a tile entity. How would I do this?

Grab the player entity, access its inventory, access the currently selected item, compare if bucket of lava, do whatever you want.

I am not home right now hence no code, but that is the process.

Is there a method to get the item held? I'm using getHeldItem() right now.

try getCurrentItem()

It's getCurrentEquippedItem(), and it works! YAY!

Now, how would I set the item that the player is holding?

use the itemstack from getCurrentItem and ether decrease it or set it too null.

So....

//stuff here
ItemStack item = player.getCurrentEquippedItem();
item.setItem(Item.bucketEmpty):
//more stuff

setItem may or may not be the right one.