I have a Nikon D3000 camera. What kind of lens do I need to capture my grandson on the football field or playing basketball, while I am sitting in the bleachers?
I am assuming your grandson is old enough to be playing his football games at night.
Shooting sports such as football and basketball from the stands is tough, but can be done. For best results you need a lens with the fastest aperture and the longest focal length that you can afford. A fast lens means one with a wide aperture that allows enough light through to let you use a fairly short (or fast) shutter speed. A zoom lens is not necessary, but is often the best solution at certain focal lengths and budget levels.
The reason that you need a fast, constant aperture lens is that most high school football stadiums and basketball gyms are fairly poorly lit. In order to use a fast enough shutter speed to freeze the sports action you need to use a fairly short shutter speed along with an ISO value in territory higher than most of us usually like to go.
If your budget allows, I would start with a 70-200mm zoom lens with a constant f/2.8 aperture. These type of lenses are not cheap. This one from Tamron runs about $1,500 in the U.S. The top Nikon 70-200mm model runs about $2,400.
I would also consider a 1.4X teleconvertor to use with that lens. The teleconvertor attaches between the lens and the body and tranforms your 70-200mm f/2.8 lens into a 100-280mm f/4 lens. This gives you more reach in exchange for one stop less light, which means you have to slow your shutter speed down to twice as long at f/4 as you could use at f/2.8.
If that is a little outside your budget, you could consider something like the Nikon 180mm f/2.8D. It is a constant focal length so you can't zoom, and it would be too long for use at close range in the gym but would work well from across court or from further back in the stands.
The problem with the more affordable consumer grade 70-300mm f/4-5.6 type lenses is that at the longest focal lengths that you would tend to use them the most for shooting football and basketball from the stands they are also very slow with a maximum aperture of only f/5.6. The difference between being able to shoot at f/2.8 and f/5.6 is the difference between a sharp image shot at 1/500 second and a blurry one shot at 1/125 second.