Bare shaft tuning and paper tuning are in essence the exact same thing, except that the paper tuning allows you to leave the fletchings on your arrow, and still see if it is coming out of the bow sideways by showing a tear in the paper to the right or left. Once you understand the concept of paper tuning, then you really don't need to paper tune anymore, but rather just bare shaft tune, as all that really matters is "Are your arrows hitting the spot you are aiming at."
Fletchings will straighten up a crooked flying arrow very quickly, hence the need to shoot thru paper. Without the fletchings, you are able to see if your arrow is coming out of the bow at an angle, so there's really no need to shoot thru paper.
In a nutshell, overspined or underspined arrows come off the riser angled to the right or the left depending on stiffness. The ultimate goal is to get an arrow which is exactly the right spine for your bow, so that it comes off the riser shooting squarely, and bends just the right amount to clear the riser without bending too much.
If you are a right handed shooter, then shafts that are too stiff will try to fly to the left of the spot you are aiming at, and too weak will try to fly to the right of the spot you are aiming at.
Arrows that are extremely weak can seem to fly extremely radical and all over the place. Arrows that are extremely stiff will still fly hard to the left, but will sometimes slap the riser on release, because there is not enough paradox for the arrow to clear the riser cleanly.
If you are a left handed shooter, expect the arrows to fly exactly the opposite of the illustration given above.
Also, if you are shooting a compound bow with an adjustable rest, all that is needed to adjust spine is to move your arrow rest to the left or right, unless your arrow is extremely over or under spined.
As arrowman states, fletchings should only be on your arrow to compensate for broadheads, or for mistakes in your release. Remove as many variables as you can from your setup, and you will in most cases shoot more accurately.