what are the Portlet methods to handle client request?

The Portlet interface defines two methods for handling requests,
the processAction method and the render method.

In addition the portlet may implement any of the 20 optional interfaces EventPortlet and ResourceServingPortlet that define the additional lifecycle methods
processEvent and serveResource

From Portlet Interface
--------------- processAction
--------------------render

From EventPortlet interface,

----------------- processEvent


From ResourceServingPortlet interface

------------------ serveResource