Fancy goldfish require high levels of dissolved oxygen in the water in order to survive or reach adulthood. Not to mention, it will keep your tank from smelling fishy. In order for this to happen 2 conditions need to be met.
Surface area, shape, and size
The first crucial part to achieving healthy oxygen levels inside your fancy goldfish aquarium is making sure that the tank is the right shape. The oxygen enters the tank from the surface. This means that the larger the portion of water that is exposed to the surface, the more oxygen will be in your aquarium. A long shallow tank will have more surface exposure, and more oxygen, then a tall deep tank. The tank shown in the picture is not suitable for goldfish because it does not have much surface area
For the best exposure to the air it's best not to use a lid. This should not be a problem as fancy goldfish are not good swimmers and cannot jump.
In order for the gas to be exchanged at the surface the water surface has to be agitated. Think about the ripples on a pond, or the waves at the beach. These are examples of surface agitation. Essentially, you are trying to mimic the surface agitation found in the wild. If your HOB filter is the right size it should provide plenty of surface agitation or aeration. However, most filters are not enough to produce good surface agitation and other methods of surface agitation should be added.
One of the most common methods used to create good surface agitation is an air pump. An air pump an an electric device that pumps air into your aquarium. An air stone is attached at the other end of the tubing attached to the pump. The air-stone creates small bubbles that float the the top and creates surface agitation. Do not misunderstand, the air pumped into the aquarium does nothing, the surface agitation does. Unfortunately, an air pump might back siphon in a power-outage and leak on the floor or electrocute you or your fish. For these reasons it is very important to either store the air-pump above the tank or to use a check valve which can be bought at most pet stores.