Level designers are an important asset to a games company, as they focus on gameplay, which is essential for playable levels. So how can you show you'll be good? Playing games is obviously a good start. Loads of them, of all different genres. As you play, take note of what makes the game good, what you find addictive. Look at styles and graphics and try to pick out what you like, and where good use has been made of the resources in the levels.

Note down what you find annoying and frustrating, and think how you could make these things better. Learn how games are made - even try talk to programmers and artists if you can, to see who puts what together in a game. Read up on the machines and technology - learn where the strengths and limitations of each format lie. Get an idea of all the elements that make a game - AI, handling, sound, music, storyline, etc...

Now start to think about your own levels using the above elements. If you can get hold of a Quake/Half-life editor like Worldcraft or something similar, try to build some levels suitable for a game - either that one, or try something different. Edit the enemies to behave how you would want them to. Make the level visually attractive, imaginative and above all, playable. If you find you're always thinking about ideas, sketching them out, and you live and breathe games.....you're making a good start! Good luck!