I am new to photography. I have a Nikon D750 with the 18-200 f/3.5-5.6 ED VRII lens on it. No filters are attached. No hood is attached. When I look through the viewfinder, it creates a circle around the outside. This appears with the camera powered on or off. The circles are bigger (worse) at 18 than they are at 200. This issue started a month ago. I tried changing the lens and the circle disappears so I know it is with this lens only. Any suggestions how to fix this problem?
The D750 is a full frame camera, while the 18-200 lens is made for DX cameras, which have a smaller sensor. So the lens can't project a big enough image onto the sensor to cover the entire sensor, which is why you see the dark circles.
The reason your other lenses don't exhibit the problem is that they are likely all FX (full frame) lenses.
The reason it used to look normal is you would have had the camera in "auto crop mode".
In the Shooting Menu, under Image area > Choose image area select "Auto DX crop".
What this mode does is recognize that you have a DX lens attached and automatically crops out the dark parts at the edges.
I'm guessing that at some point you changed this menu setting.
Don't use 18-200 3.5-5.6 ED VRII on D750. That's DX (small) lens on FX(big) camera, the result is heavy vignetting, as you describe. Or the camera switching into FX crop mode. It's pretty much "a waste of full-frame camera", as you'd get better results when using much cheaper DX body.
Get a 28-300mm f/3.5-5.6 VR instead. This is the closest FX equivalent of 18-200 on DX. As a proper FX lens, it will let you use full potential of your FX camera.
If this setup was sold to you recently, I believe you should be able to return the 18-200 lens. It's not a appropriate match for D750. If the seller told you so, he mislead you.