I have removed 100's os squares of vinyl siding and this is what I have always done:
FIRST CHECK FOR WIRES AND METERS! When it starts coming off it could go very fast.
Remove all the shutters and any other material installed over the siding.
Then, you may need a flatbar to get under the bottom of the vinyl siding and release it from the starter strip but after you do that, grab onto the bottom of the vinyl siding and pull. It should peel up the wall without any problem. Some nails will pull out and some will stay as the siding breaks around them. Once you get a good section released but still interlocked, hang onto the siding and wave your arms like you are spreading bed sheets and it should come right off.
If you are installing new vinyl siding you can just hammer the nails in that did not come out.
If you are trying to restore the old siding, plan to caulk alot of holes. You should have them between every 12 to 16 inches in width and every 8 inches in height.
Like the others have said, be prepared for anything. Your window sills may have been cut back when the siding was installed and will not look right after the siding is removed. You may find a window or door that was boarded up?