The easiest way to play Terasology is to simply use the applet link and start playing! You'll get a prompt or two to click through if you want to trust the applet to run.
Note that since we're in constant and early development existing worlds often go incompatible with later builds and you may have to clear your old data for that reason.
For the downloaded application or when running from source you can simply delete the SAVED_WORLDS subdir from the directory you stored the game in. The applet can be a little trickier as it can store stuff in a few places, like so (Win7 example):
- C:\Users\[user]\AppData\Local\Temp\lwjglcache - applet data files, usually will update fine with newer versions of the app without user interaction
- C:\Users\[user]\AppData\Roaming\.terasology - actual game data, including SAVED_WORLDS that you may need to delete manually
- C:\Users\[user]\AppData\LocalLow\Sun\Java\Deployment\log - system logging for the browser trying to load the applet may go here and can be useful for troubleshooting, but most likely you won't ever have to worry about this one