The most common cause for this is that you don't have the IIS host header configured correctly. The 404 will appear because you are hitting a different IIS web site and not the one you intended to.
If you go into IIS Manager and click on "Sites" in the right hand pane there will be a column called bindings and a column called ID.
IIS will check in the order of ID for the first site that matches. Make sure the default site is stopped. If you see bindings that look like the following:
ID 1: Bindings: *:80
ID 2: Bindings: www.yoursite.com:80
www.othersite.com will match ID 1. Any other site that doesn't specify a port or https: will be directed to ID 2. You need to ensure that the site you are trying to access matches your bindings. The "www.yoursite.com" is added to the site via "New Web Application" in SharePoint. There is a field called Host: in Central Administration. This should match what you are typing from inside and outside the server. If you need the site to respond to multiple names, you need to extend the web application.
Assuming you used the default of claims authentication, here are the instructions for that:
http://technet.microsoft.com/en-us/library/gg276325.aspx
I am not sure if this is still required in Server 2012, but disabling the loopback check might also help, although this usually results in a 401, and repeated attempts to log in. Here are the instructions for that.
http://support.microsoft.com/kb/896861