I recently bought my first DSLR, a Canon 550D with the kit lens. I want to buy an additional lens for use both indoors and outdoors, but I'm confused about what type or focal-length I should buy.
Play with the kit lens for a while. Then take a look at the photos you took, and find the ones you like. Make a list of things you like or don't like about the photos.
If most of your photos end up near the same focal length, or you keep saying "I wish the background was more blurred" you should get a prime at that focal length. Ex: EF 50mm f/1.4 USM
If you look at the photos and say "I wish I had a wider view." you might want a wide angle zoom. Ex: 10-22mm f/3.5-4.5
If you like taking photos of things far away, or like a flatter perspective in your shots a telephoto zoom might be appropriate. Ex: EF-S 55-250mm f/4-5.6 IS II
If you really like traveling light, and accept the compromises in the design, a superzoom could be good for you. When I was first getting started I borrowed a superzoom for a week and had a lot of fun wandering around town taking wildly different types of photos. Ex: EF-S 18-200mm f/3.5-5.6 IS
Have fun with your new camera. :)
Canon EF 50mm f/1.8 is probably the best one for you to learn how to shoot DSLR. You zoom with your legs and not the lens. Think about what you plan to do in 3 years time. Will you ever move to a full frame camera, if so, don't waste time buying any EF-S lenses. Yes, they may be cheaper now, but you can't use them on full frame like 5D or 1D.
For general walk around, I would suggest either the 24-70mm or 24-105mm. But those are relatively more expensive. Those two will yield probably best photos, even with 550D.
Use the kit lens until you find a situation where you can't capture the picture you intend to capture - than ask how to capture this picture.
The answer may be that you need a new lens, it may be you need lighting equipment and more often than you think the answer will be learning a new technique you can use with your existing equipment.
Buying new equipment you don't need right now is just a good way to waste money.