A great deal of porcelain carries some sort of mark to the base. The most important of these is the factory's backstamp, but some pieces have additional marks relating to design, decoration and so forth. These marks are a boon to collectors because they can help enormously with the identification and dating of a piece, and the right set of marks can sometimes make all the difference to a piece's value. There are useful online resources for researching maker's marks, but to do so effectively you first have to differentiate between the kinds of markings you are likely to encounter.
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 collectable 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 colour. 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.