Teapots are made of many different materials. Porcelain, pottery, silver, silver plate and tin are the most often used. Sizes of teapots were rounded until the mid 1700s when the pear shape became popular. By the 1800s most teapots had straight sides. Then they became round again but they were much fatter than the first ones and had a pedestal type base. Earlier Oriental pottery teapots in the early 1700s did not have glazing under the lid and around the inside of the teapot rim, as they were glazed with the lid on. Later 18th and 19th century teapots will have glazing underneath the lid and around the rim.
Determine what material the teapot was made from. Most glass and pottery is obvious but metal ones may be harder to determine. Touch a magnet to it and see if it sticks; if it doesn't, it may be silver.
Check the holes inside the pot that lead to the spout. Older ones may have only 3 holes or they may not be perfectly rounded holes.
Check to see if there are any names, trademarks or other lettering or numbers on the bottom of the teapot. Any of these marks could lead you to the manufacturer.
Compare the teapot to pictures of teapots in antiques and collectibles magazines and books. Also check online at sites that sell antiques. The type of spout and the design of the teapot will help you to determine what year it was made.
Compare the weight of the teapot to that of modern ones. An older pot will be much heavier. Size may be another clue: teapots from the 18th century were smaller because tea was expensive and only small amounts were brewed.