To get started, I recommend you do quite a bit of research.
First, browse through the NSF GRFP website thoroughly. Make note of the application deadlines (they're different depending on your field and reference writers have separate deadlines). Check out the applicant resources, which include Frequently Asked Questions and contact information for people that are experienced with the GRFP (likely even at your university!). Then, create a FastLane account. You will submit everything required for your application through FastLane.
Start thinking about who you will ask to write your reference letters. Only three are required but you are allowed up to four. Get all four references; you don't want to be that person who is disqualified because their third reference letter was never received. You have to rank the letters in the order you wish them to be considered by the application reviewers.
Next, Google "NSF GRFP Help" or something similar to find other resources on the web. Many fellows publish blogs and personal websites with information that you may find useful. I used this one by Alex Lang most extensively. I found his database of example statements and links to other blogs particularly useful.
Speaking of which, read examples of successful statements and reviewer feedback to get an idea of what the reviewers are looking for. Be aware that, starting with the 2014 GRFP application, the Previous Research Statement and Personal Statement were combined into one, 3-page Personal, Relevant Background, and Future Goals Statement. However, older sample statements will definitely still be useful. I provide mine later in this guide, but the aforementioned website has a database with plenty.
If you use social media, follow NSF GRFP on Twitter as they often provide updates there in addition to the official website. They even sometimes tweet interesting interviews and other application resources.
If you've gotten this far, it's a good time to become very familiar with the merit criteria. Every aspect of your application depends on them.