There are a lot of excellent articles for tuning bows but most relate to tuning for release shooters. Some times  comprehensive archery books you can find an area that relates to finger shooting set up. While I have tried several ways to tune for me this is the easiest. 

I will relate this to you the easiest way that I know how. Remember though there are many factors that one must consider.

A list of these would include;  Proper arrow spine, right arrow length, weight of point or broad head, length of bow, hand placement and do not forget a clean   release.  What I am going to describe is going to be applied to the shooting of a compound bow.

Most bows today are cut past center and that makes life easier.
What you will need is this: Your bow, arrow rest w/side pressure and vertical movement, a Golden Key enter gauge and a set of allen wrenches along with an arrow. With this equipment you can tune your bow in perhaps a half-hour of shooting.

Go to your local archery shop and ask for a good finger shooting rest.
Golden Key makes several.     The huntmaster 2000 is an excellent choice. New Archery products center plunger rest, Tiger Tough Deluxe star or the Cavalier Free Flight all are good choices. Install these per manufacturer instructions. A few things to watch for: make sure the arrow, when placed on the rest covers the plunger hole and/ or the plunger/ side pressure plate goes between the fletching as the arrow passes.

Next: install a peep into the string, there is no need to tie it in as yet.
To adjust the rest: plunger for center shot use the center gauge. Place the arrow in the rest and using the gauge you can see if the front end of the arrow is lined up left or right of the arrow sitting on the string. If not you an move the plunger, or the rest until the tip of the arrow is lined up perfectly with the string. Now you can look at the bow from behind and see if the string bisects thew arrow from back to front, doing so the peep should be over the center of the arrow about half way down the shaft. ( See picture below.)

If not, adjust side tension or move the rest accordingly.  Depending on the finger pressure as you shoot or the placement of your hand on the grip this might change but now we have a starting point.

Let us see this from the pictures angle.   The string dissects the middle of the grip.  Usually the string is located on the centerline of the grip which is located on the centerline of the bow. Now you are almost ready to shoot. Loosely tie in the peep sight, you might have to change position later. Have someone stand in back of you as you shoot.

You should NOT be watching the arrow but your friend or spouse do that. If they see the arrow fishtailing then adjust the rest or plunger until it no longer fishtails. If you are using a plunger DO NOT MOVE THE REST! By increasing or decreasing the plunger tension you can get your arrow to fly straight. You can look at the relationship between front and back end of arrow in the target butt. That also indicates how the arrow is flying. When you are close to a straight flying arrow you can sometimes adjust the flight by turning your lim bolt in half turns either way until you reach the optimum arrow flight.

The weakest link in this is YOU. There is no question that a mechanical release will make you a better shooter. But what if it is broken or lost?   What do you do now?

If you constantly practice with fingers you can be deadly accurate. Becoming familiar with your equipment will make you a more consistent shooter under bowhunting conditions. Finger shooting is alive and well.    Fred Bear did it, Howard Hill did it, Robin Hood did it, Ben Pearson did it, Byron Ferguson shoots arrows through wedding bands at 50 yards using fingers.  From the primitive cave man to the twentieth century the bowstring and the fingers can still be used together. There is something special to watch the arrow fly when relaxing your fingers and watching the view from behind the string!

That is how I see it in my "view from the back of the string".