What are the differences between collectible teapots and the ordinary ones you have sitting atop your stove? That question will yield a different answer depending on who you ask.
However, the overall characteristics of a teapot that is collectible is that it is very well made, extremely hard to find, and widely envied by established collectors.
Though tea drinking got its start in the Far East in the early centuries, teapots were not around at the time. The Chinese used handle-less cups to brew loose-leaf tea and drink it. Many years later, the teapot as we know it was invented, and western countries like Great Britain and the United States are credited with the invention. Teapot collecting has come to include all tea brewing and drinking vessels.
Collectible teapots are sometimes known as novelty teapots, although this usually refers to vessels which have an atypical design feature. With the internet now in high gear, it is very easy to get in touch with other collectors and enthusiasts around the world and thus become more educated on teapots. Education, in fact, is a great first step if you want to get into novelty teapots.
So how do you get that education? One piece of advice is to log onto eBay and keep a close eye on how the various types of teapots sell. By and large the experts in the industry are also very willing to help you, but getting out and learning some things on your own will help you retain the information.
On the other hand, you can simply collect teapots the way you want to. Pick a style or type of teapot that you are most interested in. It could be a design theme, a country of origin, or even a certain layout in terms of physical style (Chinese, British, American, etc). Each teapot type offers a unique quality and experience.
Themes are easy since companies like Carters Teapots have created a number of novelty teapots made for collecting. For instance, transportation themes are common since teapots are made to transport liquid. These companies also encourage collecting by making only limited numbers of each design so that the value will grow more quickly.
You may also decide to pursue antique and historically significant teapots. You could concentrate on an era. For instance, in the 19th century, many companies began to make fine teapots to be used for formal occasions. One such company, Minton, began to design some classic teapot forms like the Chinaman, the monkey, or the old "tortoise look" standby. With those classic designs out there, you will surely see that 19th century teapots are something to fall in love with.
Similarly you could look to the 20th century, or even to specific countries. China and Britain both have a long history in tea drinking and thus teapots. You just have to decide what you are looking for and what price you are willing to spend to get your own unique collectible teapots.