The solution is called paper tuning, what you do is shoot your arrow completely through a sheet of paper and examine the hole left behind. The easy way to do this is to tack a sheet of paper to a large empty picture frame and stand it up about 1.5 arrow lengths from the target.
This is what it should look like, three equal length slits from the arrow feathers and one nice round hole from the shaft.
If it's flying off center, the feather holes will be shorter and the hole made by the shaft will be long instead of round.
In this case, it's because the arrow is flying nose up instead of straight inline.
In order to fix this, you move the nocking point/knocking loop up or down and the in the same direction the shaft hole is pointing while the arrow rest moves the opposite way.
In the example above, the problem is caused by the tip being higher than the nock when fired, so you need to move the nocking point up. If the shaft hole is pointing left, then the rest needs to be moved to the right in order to bring the arrow into line.
It's also possible that the yokes on a compound bow are out of tune and need to be adjusted so that the string is in line with the wheels.
Finally, if the tear is at an angle, its recommended to fix the up and down first.