Don't even try to tell us that you haven't wondered about this one.
The secret to the bird is not, in fact, patenting and selling such a useless invention. (That distinction, I believe, is held by the person who invented pet rocks. Kudos, whoever you are.) It is choosing the right liquid to fill the bird with. The commercial birds are filled with methylene chloride, but it could be any liquid that turns to vapor at low temperatures.
After that, all it takes is measuring the right proportions of the two bulbs and the tube that separates them. The tube should extend almost entirely into the lower bulb.
To understand how the bird works, it is necessary to understand that even though we don't notice the air and liquid vapor around us in daily life, they exert pressure on the things around them. At times, that pressure can be extreme, counteracting even the force of the earth's gravity.
When left to themselves, the vapor and the liquid inside the tube are in an equilibrium that allows the bird to rest in an upright position. To change that, we dip the bird's head – usually covered in some kind of fabric - in water. As the water evaporates from around the head, it takes energy with it, and the head cools down.
The vapor inside the head cools and contracts. Since the glass around the vapor won't contract, a vacuum is created inside the head of the bird. The liquid is the only thing that can give, and it does. Liquid from the lower half of the bird is sucked up into the head of the bird like red-shirted Star Trek extras during a hull breach.
The head of the bird is now too heavy for it to stay upright, and the bird dips forward. As it dips, a corridor is opened up between the head and the body of the bird. The vacuum can more easily suck the vapor than the liquid and vapor travels to the head until the pressure is equalized. The liquid drains back to the body of the bird, making the lower bulb heavier. The bird it tipped backwards and returns to its full upright position in.
That is, until more water evaporates from fuzzy head and the cycle is started over. By allowing the beak of the bird to dip in water, there is a continuous supply of water soaking into the head of the bird, and it seems to move on its own far longer would be possible if it were just swinging due to someone pushing it once.
Then it's all over, except for the marketing campaign. Personally, I think it's the top hat that did it.