This is an easy way to add your site or index your site by google.
This maybe the easiest but not the fastest okay.
So here is the Step by step Guide on How to Add your Site or Blog to Google
Step 1: Go to http://www.google.com/addurl/?continue=/addurl
Step 2: Just Put you Site URL on the Box
Step 3: Fill up the verification code
Step 4: Send it and its Done.
Hope this help :D