Changing fields after PhD?
The most typical path for shifting your field after a Ph.D. is by means of one or more postdocs.  A postdoc is an opportunity for more training and is often used by people to move between fields.  

The challenge is finding the right postdoc (or chain of postdocs) to make the shift, which may be easy or difficult depending on the particulars of your fields. For example, shifting from computer science to systems biology is generally pretty easy; moving from Sanskrit literature to aerospace engineering would probably be quite difficult.

Once you have a more more permanent position, on the other hand, you are likely to find much of your time is consumed by the other responsibilities of that position.  For example,  if hired as faculty you will find much of your time is spent not as a researcher but as a teacher, advisor, department committee member, fundraiser, and administrator.  Combine that with something like a ticking tenure clock, and it can be quite difficult to change fields once you have passed the postdoc phase.