So you've just bought yourself a brand new DSLR (Digital SLR).  You love it, you've finally overcome the problems with traditional point and shoot digital cameras of the action being out of frame by the time the actual picture was taken.  The only problem you've discovered is that you're severely lacking in zoom, the lens that came with the camera, the "kit lens" just isn't cutting it anymore.

Thankfully you own a DSLR, the solution is easy, buy another lens!

Now we run into the problems of choice. 

When chosing the new lens you wish to buy there are several important factors that you need to keep in mind.

Firstly the focal length of the lens -  This is normally expressed in terms of mm. e.g. 70-200mm of 17-55mm.  This is an indication of the zoom that can be achieved by the lens.  The larger the higher number the more zoom, the lower the lower number the wider angle the lens is able to capture.

The maximum aperture of the lens -  Just to confuse you the small the number following the f found in most zoom lens descriptions the larger the aperture.  The value of a larger aperture is that in low light conditions, a large aperture will allow more light through onto the sensor (think... film) and thus allow a higher shutter speed at a lower iso setting (better quality, less noisy image).

The mount - DSLR lenses come in a variety of different mounts, primarily designed to fit different sorts of cameras.  Make sure that the lens you are looking at is available in the mount required for your camera.  Generic lenses manufactured by companies such as Tamron, Tokina and Sigma are typically available in a variety of mounts where as Canon and Nikon lenses generally fit only on the camera's of the same company.  Be aware that manufacturers may have more than one type of mount for instance Canon has and FD mount (old style) and EF mount (current mount system).  The two aren't compatible.

Quality - The components that make up a lens are of great importance in the overall performance, low quality glass or plastic components are not a recipe for a great image.  Similarly poor build quality means that you are unlikely to enjoy a good time with the lens.  Theres no real way to know these aspects of a lens without trying it, so make sure to read a lot of reviews on the internet.  Read both ones taken from a scientific view and consumer views to cover all aspects of a lens.

Keep in mind that a good quality lens is going to last a lot longer than your camera body so spending a little more on quality may pay off in the long run.  The upper bracket of lenses also maintain their resale value well.