How do I customize the Fivestar module? I need to customize part of the Fivestar module's output, so that I am able to assign points ( e.g. 1, 2, 3, 4, 5).

I want the module to sum up and display the total points received by the content or user, and I want to use my own icons in the widgets.

Is this possible? 

I am using Drupal 7.
Your first two items are settings that can be configured on the Fivestar CCK field's display options. You should read through the Fivestar Documentation thoroughly for instructions on how to set up a rating system.

If you want to use star icons of your own, you can simply override the styling of the Fivestar widget in your theme using CSS. However, if you want to create a star set that can be easily reused across sites, you can follow the instructions for creating a fivestar widget set