You can also down load the user manual from the Nikon USA site. At the same site you can look at the camera's detailed description and specifications for the camera that includes the compatible lenses and any problem lenses
The lens to watch out for are the pre-AI lenses that do not have the Aperture Indexing ring or indent and do not have the electric contacts. Some of these lenses can be modified to work with AI cameras.
#2. "RE: Which lenses will fit - if any?? D3000 or D5000" In response to Reply # 0
Both lenses will physically fit on either the D3000 or the D5000.
The Nikkor will not autofocus on either camera, and unless the Sigma is one of the latest versions (i.e. bought new within the past year or so), it won't either. Cameras like the D3000, D5000 and the new D3100 require lenses with their own AF motor in order to provide autofocus.
The list linked to in the earlier reply contains all such lenses, but be careful to read the full titles of the lenses; some are pretty similar to earlier versions (like, I think, your Sigma) that don't have motors.