Like all animals goldfish need air in order to live. Because water is thicker than air it makes absorption and extraction of air more difficult from it. Fish have gills, which are surprisingly more efficient than lungs are in the way that they work. Gills are rich with filaments that provide deoxygenated blood flow to the gill’s surface and lamellae. Lamellae are the part of the gills where gas exchange take place.
In order for a goldfish to breathe properly they need a great deal of air. Air is disolved into the water and gas exchange can occur in.
The first is water surface area. The larger surface area water is exposed to open air the more oxygen can be disolved. Coincidentally surface agitation will also cause this to occur more efficiently. Providing your goldfish with a wider tank will allow for more oxygen to be absorbed in the water.
The second way to maximise the amount of oxygen in your tank is by purchasing an air pump, airline tubing and a air stone. When looking for an air pump you want to find a pump rated higher than your tank’s water volume. It is better to over aerate than to under. Make sure your air stone is placed at the bottom of the tank. The longer the bubbles take to reach the surface the better it will be.
Keep in mind that you must store your air pump higher than your tank in case the power goes out. In the case that your pump shuts down your airline tubing will create a suction and water will be pulled through and towards your pump and destroy it. A way to combat this if you cannot get your pump higher than your tank is to purchase a check valve. They cost less than a dollar and installed properly can save your pump from severe water damage.