Instructions
Look at the base of the vase. The maker's backstamp usually consists of the name or the initials of the company, often combined with some pictorial element. It can be printed or impressed. Most long-standing companies would update the design of their backstamp over time, and this can be an important dating tool for collectors.
Look for any additional names or initials. This will be the name of an artist or designer who has contributed to the piece. Some of these can be collectible in their own right. You will find information on designers in specialist guides to a particular pottery.
See if there is any kind of painted mark, even if it's just an illegible dab of color. This is a painter's mark -- a sign that the piece has been decorated by hand. Such a mark is always nice to see, as it's a sign of quality.