Sign up for Slicehost and work through the articles. They will take you, step by step, from a new slice to a hosted application. Two months ago, I was in the same position you are. I now have three slices all running apps. I have learnt about load balancing, database administration and tuning, web server configuration, the inner workings of Linux, scheduling, bash...

At times, system administration will make you want to kill yourself, but it's worth learning. Building your own slice is a great way to start.