I've followed this tutorial: http://anandhansubbiah.com/blog/writing-your-first-android-application/, but no matter what I do, and what I change, when I run the app, all I see is the image below. Is there something I must press to start developing? Did I add starting code. I'm completely stumped...
You don't have to press anything, and your code shouldn't be able to cause that. It looks like something's wrong with your emulator.
The SDK comes with a few tools you can use to try and figure out what's going on and fix it.
adb is the debug bridge - use adb logcat to see logs from the device. I don't think it will connect with the emulator in that state, but you might as well give it a try anyway.
android is the main AVD manager, and you can use it to create new virtual devices and see details if they failed to load.
If neither produce anything useful or obviously wrong with your virtual device, you might want to try just creating a new AVD in the manager and using that instead. You may also want to try starting the emulator yourself instead of letting Eclipse do it, just in case it's doing something to break it. Use the emulator tool in the SDK to do that.
From you're screenshot it appears the emulator hasn't fully started so it's unlikely to be a problem with your app. It can take a while to start so leave it for a few minutes just to be sure it's not slow. If that doesn't work try recreating the AVD.
Once the AVD is running you can redeploy your app to it as often as you want so there's no need restart it.