How to use the buttons on the side of my 55 to 200 lens for my Nikon D3000?

There's one thats says 'A' & 'M'
And one that says "VR" and you can turn it off and on. What are these for? C

The manual sez…

A = autofocus M = manual focus. Therefore A/M = autofocus with manual focus override.

VR = vibration reduction. Reduces camera shake from your inability to hold your camera steady.

Nikon recommends that you turn VR on AFTER you turn the camera on, and OFF before turning the camera off. While this is not critical, it does prevent the lens VR mechanism from making a banging sound when the power is off and you are moving the lens (in other words, turning the VR off first locks it in place).

Use VR when you are worried about camera shake. But always turn VR off when you are using a tripod.

Again, refer to your manual. It is highly detailed and will tell you what situations to use these controls.

A is for auto-focus and M is for manual focus

VR is the image stabilization mode when you are shooting photos at shutter speeds usually too slow to shoot hand held without adding some kind of blur caused by the cameras movement

If you are using shutter speeds faster than 1/250th second or have your camera on a tripod, you do not need to use VR.

Here is a sample of a shot taken at night using a 300 mm lens with the VR turned off.

If you look at the photo information, you will see the settings used for that shot