You can put the action name and method to be executed into a Map.
So you can have
where actions is a HashMap that contains your action name as keys and the value will be a method name to be executed.
execute - this is the method that delegates the execution. But here you will need reflection and it gets really complicated if the methods return different types of objects and take different parameters.
James said
you should use Struts. I say the same or Spring MVC or one of the many frameworks.
Or if you don't want to introduce them then download the sources of either Struts or Spring and take a look at the DispatchAction, LookupDispatchAction in Struts and MultiActionController implementations in Spring. These should give you an idea on how to implement in a good way.