If you just got your DSLR, it most likely came with a kit zoom lens. Since it's most likely a zoom lens, it is good enough for you to get started with. It will give you a good range and you should really not invest in more lenses until you are confident with your camera skills (know your way around your camera). Just because you might not really know what lens will compliment your camera and existing lens collection. This will allow you to assess what adjustments or improvements in your lens collection should be made.
As a photography beginner, basically you will want to have the least amount of lenses to cover a wide range, 10-300mm to start with. This will help when you are traveling a lot, in which case most photographers do. If you mainly shoot in a studio or somewhere where you can just leave your gear and not have to carry them around, then you can expand beyond what you can carry. So say, if my kit lens came with the shorter end 18-105mm, then I will want to get a 70mm-200mm (or even 300mm). This would cover the ranges for any situation. Nothing will be too far, or too close for me to take a photo of. It is a good base to expand your lens collection.
If you are looking to expand your lens collection, think about what camera you are using. Weather it's a Cropped Sensor or a Full Frame. Most entry level cameras today are cropped sensor cameras and will come with a crop sensor kit lens. This means that if you ever change to a full frame camera later on, you may be able to use your crop sensor lenses but your photos will have a black ring around it from the barrel of the crop sensor lens. Some newer full frame cameras will automatically crop your pictures if you are using a crop sensor lens. In my experience, it would make sense to have full frame lenses rather than cropped lenses. As full frame lenses will work well with both without the black sniper scope effect.
Photographers have a saying, "If you have to use the zoom function, you are not close enough" to the subject to get a really got picture(even if you zoom all the way in). You end up losing quality compared to photographing as close as you can. Another problem with zoom lenses is that the barrels extend and you would be losing a lot of light the farther you zoom in. This is where Prime Lenses are very nice to have. There are lenses out there with apertures that remain constant through out it's range. And although they may be a little pricey, they are very nice to have.
Prime lenses however may not be as pricey, they provide a lot of light at it's widest aperture and often are very nice pieces of glass. So which Prime Lens should you get? It depends on what you do. For portraits, 50mm, 85mm and 105mm are very nice focal lengths to have. If you are on a cropped sensor camera, a 50mm full frame lens will be approximately equivalent to between 75mm - 85mm depending on your camera. For landscape photography, a wide 35mm prime lense will also be nice.
Having a collection of good lenses with a combination of a wide range will allow you to take good pictures anytime, anywhere. Investing in glass is paramount to investing in camera bodies if you are serious about taking your photography to the next level. So what lens should you get next? A lens that does covers the range that your lens/es currently does not, or one of the primes.