Today I found a better way to do it, thanks to this post on StackOverflow. You'll have to modify the steps that the poster follows, though, mostly because you can't log in as root on an Amazon Linux instance, but everything is available using sudo.
First you have to set up an instance (use a Large instance, you won't regret it), and the easiest way to do that is through the Amazon Management Console. Once you have your instance running and you can log in, do the following:
First, add the official Mono repository to yum. I'm quite new to yum, but the SO post made it quite clear. In your home directory, issue the command 'vi mono.repo', and press 'i' to enter 'insert mode', then paste the following snippet:
Then, press the 'escape' key, and type ':w' and ':q'. I'm not used to vi, but I know it's on there and this happens to work. Now you have the repo file in your home directory and you need to move it to the /etc/yum.repos.d directory, but only root can do that, so issue the command 'sudo mv mono.repo /etc/yum.repos.d'.
Next, you'll need to clear the cache using 'sudo yum clean' and install the Mono stack using 'sudo yum install monotools-addon-server'. That will install the latest stable version of Mono, currently 2.10.1.
You can do this on a Large instance and make it quicker, then shutdown your instance, make a snapshot, terminate the instance and make a new 'Micro' instance using the instance and you'll be set up. For some funny reason Micro instances are 64-bit and Large instances are too, but Normal instances are 32-bit only.
Now I have to figure out how to set up a decent web server so I can try to get ASP.NET MVC going.
UPDATE: I definitely needed the following to make ASP.NET MVC work: I had to install WCF, by issuing this command: ‘sudo yum install mono-addon-wcf’. The mod_mono module is autohosting, which means that when installed, it automatically loads so ASP.NET should work out of the box, and the example site is located at /opt/novell/mono/lib/xsp/test.