There are a few things one need before making a game with XNA.

You will need either Microsoft's Visual Studio or Visual C# Express, the latter being free to all (follow the link to download Visual C# Express.)

Then you need to grab Microsoft XNA Game Studio 3.1

Ok, so you will need a windows box for this (Windows 7, Windows Vista, or Windows XP.) If you have a mac, then you will have to acquire a license for windows and install it, either on a Virtual Machine or via BootCamp. XNA will certainly work on a BootCamp Partition and with the latest version of Parallels Desktop for Mac.

There are some great resources for learning this environment. XNA Creator's Club is a wonderful resource. There is also a wonderful book available from O'Reilly, "Learning XNA 3.0", by Aaron Reed. You can purchase a PDF version of the book for $27.99, but there is also quite a bit of sample code on Mr. Reed's site.

I will post some of my sample code here a bit later.

Good Luck.

Oh, as a post script, it will be possible to stream some of your games via Microsoft's SilverLight. I will hopefully have a tutorial set up for that by next weeks class. Cheerio.