Every EC2 instance has about 150GB of transient disk space. It works like a regular disk but once you shutdown the instance (or in the rare event the instance fails) the disk is gone forever. To solve this problem, Amazon provides EBS volumes ("elastic block storage"). These are like raw disks that you can create on the fly. You create one, attach it to your instances, give it a filesystem, and then mount it.

You can run MySQL off of the transient disk ("/mnt") but you should consider running it off of an EBS volume. One reason is because you won't lose the disk if something happens to the instance. Another is that you can use the snapshots feature to create instant backups of your database. Later on you can create new EBS volumes from a snapshot (which is really cool for building a stage environment with production data).

This may sound a bit complicated when you're just starting out. It was for me anyway so after working with AWS for a couple years I started working on a development and deployment tool for EC2. The configuration is entirely via a Ruby DSL.

You define the properties of your environments and roles with the machines DSL (including EBS volumes) and you script your repeatable processes (like deployments) with the routines DSL:

http://github.com/solutious/rudy/blob/0.7/Rudyfile

If Python is more your style, there's boto: http://code.google.com/p/boto/