How do you make a module integrate with the Rules module? Rules has so many uses but if another module is not integrated to it, you can not use rules with it. Does anyone know how to integrate a module with rules? 

The module I would like to integrate is Metatags.
The best documentation you will find is in http://drupalcode.org/project/rules.git/blob/refs/tags/7.x-2.1:/rules.api.php. You will also find this file in the code you downloaded from drupal.org.

You also would probably learn something from looking at other modules that implement rules similar to how you would like it in metatags and seeing how they implement the above hooks.

Then it is up to you do decide what functionality from metatags you want to expose to rules using those hooks.