Will a Minolta MD: Vivitar 70-150mm F3.8 work on my nikon D3000?

What about this one:

Vivitar 70-150mm, 1:3.8, K/AR.

No. You'd need a MD to f mount converter. Most likely a nikon 55-200 would be not that much more expensive and work a whole load better.

You can buy an adapter to use either the Minolta mount lens or Pentax mount lens on your D3000 but in my opinion its not worth the trouble. You'll have no auto focus and most likely you'll be limited to stop-down metering.

To meter using stop-down metering you have to have the lens wide-open at its maximum aperture so you can compose your picture. You then stop-down the lens to the aperture you want to use to take the picture. As you stop-down you'll see the viewfinder getting darker and darker - how much darker depending on the taking aperture. You then set the shutter speed to get a correct exposure.

So if you decide that f11 is the aperture you want to use to take a picture you'll compose at f3.8 and then stop-down to f11, check the shutter speed, set it and then release the shutter.

Just buy a comparable Nikon AF-S lens for your D3000 and you'll be much happier.