I have created a test website that contains a single ASP.net index.aspx file that contains a gridview listing information from a MSSQL database.
I would like to have this made available as a webpart on our sharepoint intranet, how would I go about doing that?
You will need to create a web part from the page you already have.
I would suggest isolating your gridview in a user control (ascx) instead of directly on the aspx page, it will be easier to use it in a web part that way.
To create a web part, you should probably start by downloading WSPBuilder or a similar tool that will do most of the work for you.
The following tutorial will give you the information you need on how to create a web part from a user control.
You should have no problem linking to your database or anything else. A web part behaves just like a user control.
You can just put your page under Template/Layouts and attach it to some SharePoint master page. It will look and feel like a regular SharePoint page.
Of course, that is good if you're into the quick&dirty approach :)