What kind of lenses can you get for a Nikon D3000?

I bought a Nikon D3000 about… 3 or 4 months ago. And I really like it.
But I want some lenses to go with it. I'm new to the whole DSLR camera and stuff.
All of my others are just a little point and shoot.
I don't know if you can use any type of lenses? Or if you have to have a specific kind that will fit your camera?

It has to be nikon mount. For autofocus to work it has to be motorized such as nikon's AF-S.

Without knowing what you're not getting from your kitlens it's a bit tricky to be more specific.

All current Nikkor AF-S lenses will fit

here is a description of all lenses that will fit/not fit
AF-S, AF-I: All functions supported
IX Nikkor lenses can't be used
Electronic Rangefinder usable with lens with maximum aperture of f/5.6 or faster
Type G or D AF NIKKOR not equipped with an autofocus motor: All functions supported except autofocus
AF-NIKKOR for F3AF not supported
Type D PC NIKKOR: All functions supported except some shooting modes
Non-Type G or D AF NIKKOR not equipped with an autofocus motor: All functions supported except 3D color matrix metering II and autofocus
AI-P NIKKOR: All functions supported except 3D color matrix metering II
Non-CPU: Autofocus not supported. Can be used in exposure mode d, but exposure meter does not function

from the nikon website
http://www.nikonusa.com/....TechSpecs

You want newer lens that has motor build in, recommended lens

Nokia 35mm f1.8
Nokia 55-200mm

All Nikon AF-S lenses will be compatible with your camera. You can consider a zoom lens like 55-250mm or a Nikon 60mm for macro shooting

All Nikon F mount, with the exception of a few early ones, will fit your camera but you sacrifice most if not all functions, but a genuine Nikon lens like the 18-135 and you will get great pictures