The modern teapot design came into existence during the Ming Dynasty. The people referred to this new style of teapot as a "YiXing Teapot" because they came from the YiXing Province of China. This style of teapot became incredibly popular, and many crafters still create replicas of the originals today. It can be difficult to identify an authentic Ming Dynasty-era YiXing pot, but there are some key identifiers for the original pots. The easiest Ming Dynasty teapots to identify are the pots with the mark of the old masters.
Look over the surface of the teapot in soft light. The zisha clay in the pot should have a purple hue. Dirt and gloss coating may obscure the true colour of the pot, so you may have to lightly clean the pot with a damp cloth (free of cleaning chemicals) to bring out the true colour of the zisha.
Examine the shape of the spout on the pot. All authentic YiXing teapots have a curved spout. It will curve at least once, but in some cases, the pots will have two gentle curves on the spout.
Lift the teapot and search the surface carefully for light fingerprints in the surface of the clay. All authentic Ming Dynasty teapots will have light finger marks because the artists constructed the pots all by hand.
Pull the lid off the top of the pot. Examine the inside of the pot for brush marks left by the pottery wheel. If you find any, the pot is a fake. Some knock-off YiXing pots will forget to remove pottery wheel construction marks on the inside of the pot, which betrays the creator and exposes a fake teapot.
Measure the circumference of the handle at the top and at the bottom. Authentic teapots always have a thinner handle near the top than at the bottom. Ming Dynasty teapots will either have their handles on the side or the top of the teapot depending on the era (both brewing pots and boiling pots came into vogue during the Ming Dynasty).
Remove the lid from the teapot and turn it over. Examine the underside of the pot for marks left by the original artists. Take a picture of the signature and take it to an antique dealer so they can determine whether the signature belongs to an old master crafter such as Hui Mengchen or Shi Peng (see reference below for full list of YiXing teapot crafters of the Ming Dynasty).
Some authentic YiXing pots of the Ming Dynasty don't have a name or any defining marks that would point to an artist. This does not mean the pots are fake; you may actually have a pot by the original creator of the YiXing pot (the artist was an unnamed monk). It may require a specialist to identify these pots.