First Thing's First: Things You'll Need

Alright, so, I decided that I would make a list of things that are necessary to get the Appstore up and working.

1. An Android Phone (Obviously)
2. A carrier that supports the installation of non-market applications.  The Amazon Appstore isn't actually in the Android Market, so you need to be able to "sideload" Android Applications.
3. An Amazon.com account.  No purchase is required to create an account, but they have some incredible deals, so I highly suggest you create one, even if you're not going to be using the Appstore.  
4. An active data or wi-fi connection.  

Okay, so, to install the appstore on your phone, you need to go to this link.  On the top right side of the page, enter either your mobile number or email address in the box.  It should send you a link to download the application.  

If you need help installing it, click here. (Credit to Amazon for the link)

Okiedoke.  That should get you all set up.  Feel free to comment with any questions.