You can use this lens, but since the D3200 does not have the AF motor built into the camera, you'll need to manually focus. To have autofocus on your camera, you need to use a lens noted as AF-S
As for the difference between D and G lenses (from Nikon USA)...
D-Type NIKKOR Lenses
A D-type lens relays subject-to-camera-distance information to Nikon D-SLRs that feature 3D Color Matrix Metering (all versions), 3D Matrix Metering, 3D Multi-Sensor Balanced Fill-Flash and i-TTL Balanced Fill-Flash. Many D-Type lenses have an aperture control ring and can be used on older Nikon SLR cameras that allow for manual control of the aperture, as well as on D-SLRs—especially useful for adjusting aperture while recording D-Movies on higher end models. When used on a D-SLR, the aperture control ring needs to be locked at the smallest possible aperture (generally designated in orange), and the aperture control is maintained through the camera's command dial.
G-Type NIKKOR Lenses
A G-type lens does not have an aperture control ring and are intended for use on Nikon D-SLRs that allow the lens aperture to be adjusted via the camera's command dial. Because G-type lenses relay subject-to-camera-distance information to the camera, where it is used to help determine ambient and flash exposure, they are also considered to be D-type lenses. The lack of an aperture control ring is perhaps the easiest way that you can tell if a lens is a G-Type NIKKOR or not.