Small papyri fragments like P52 cannot be dated using conventional means such as carbon dating, as too much of the sample would be required. Instead they are dated using a process known as Palaeographic Dating. This process is incredibly skillful as it requires the Palaeographer to posess an in-depth knowledge of the language being studied. It is also important to know the historical usages of various styles of handwriting, common writing customs and scribal or notorial abbreviations.
A good knowledge of writing materials is also helpful as the type of pen, ink and paper (or papyri, velum and parchment) used can be a good indication of when something is written.
All of this makes Palaeography a very difficult art to master and also one which is never fully learned but always evolving.