If you are an Arduino beginner and don't have other programming experience this will be a major challenge. In addition to the navigation issues there are many other features - electrical and mechanical as well as programming - that need to work to achieve a finished product.
Start by working through several of the example programs that come with the Arduino IDE.
As far as the navigation is concerned, what sort of space will the robot be working in? A large room with table-tennis tables and few other obstacles?
Ping pong balls are very localized things (compared with mowing a lawn or cleaning a floor). I wonder is it sensible to do anything other than identify them visually which is beyond the capacity of an Arduino. A rotatable camera should find them very quickly with a minimum of movement by the robot.
...R