Zoom lense won't focus on camera? What's wrong with it?

Not sure what model but on my moms nikon camera (might me the d3000 not sure though) when we put the zoom lense on and it just goes back and forth trying to focus but is always really blurry and it won't take pictures cause it can't focus. Is there a setting on the camera we have wrong or we need to take the lense to a camera store to have it fixed? How much will that cost?

Added (1). Also how do you increase shutter speed?

First, it's lens, not lense. Second, make sure you are using the camera in a bright place, or use the flash.

Try cleaning the contacts on the back element of the lens. You could also try switching it to Manual Focus and then back to Auto Focus. Has your lens been out in the rain or dropped at all recently? If you can't get it to work, take it into a store and ask how much they would charge for a repair. If it is anywhere near £50, buy a new one. If you have the D3000 you probably have the 18-55mm kit lens.brand new, this lens costs around £80. Hope this helps.

If you want to change the shutter speed, one way would be to select the [S] on the top of the camera, look through the view-finder and scroll the wheel. You should see the number change. This is your shutter speed.

Without knowing the lens in question, it is hard to say… BUT, every lens has a minimum focal distance.

For example, the minimum focal distance for:

18-55mm f/3.5-5.6G ED II AF-S DX is 11" (28 cm)
70-300mm f/4-5.6G it is 4.92' (1.5m)
55-200mm f/4-5.6G ED AF-S DX is 3.1' (94.49 cm)

Also, the amount of available light can affect the ability of a lens to auto focus (some need more light than others).

To increase your shutter speed, refer to the manual. If you don't have it, it can be found on the Nikon website.