A bucket (cat walking into frame optional)
Open up that sink door and take a peek at what you see. It should hopefully look like this. If you have metally looking pipes instead of plastic ones, you might need a wrench of some kind. The little U shape is the trap where your earring should be. It is filled with water (and probably some other gross stuff, but try not to think about that).
Clear away all of the stuff under the sink and position the bucket under your pipes.
There's a little ring on the back end of the U. Give it a twist. Mine was pretty easy to loosen. If it's tight you could probably use a wrench. As you can see in the picture the ring will slide up and the U will slide away.
From there you can just kind of tug the other end of the U off. Warning: it is filled with water and smells kind of gross. Another purpose of the U tube besides being a catch, is that it stays filled with water and keeps the sewery smell from coming up the pipes into your bathroom. Anyways, tug the whole U thing off.