That is evident of a out of tuned bow. You have no choice but to tune your bow and if you don't have access to the laser/levels used for tuning or paper tuning, you need get to a shop that can.
If you wish to try at home without the use of said tools, the arrow needs to come out of the bow centered on the string, not pointing left or right of the string, that's usually an indicated by tail whip. Having the arrow come off the string perpendicular to the string (up/down, level) isn't as important as center shot. Many archers prefer a slight nock high depending on bow model.
To get center shot at home you can A. eye ball it, the center of the bow should be centered on a imaginary line from the center of the limb bolts for example. B. you could run a string from the center of the limb bolts and try to center it on your arrows center. That should get you close.
Start from there. If you notice your arrow points out or in from that center line, that is not a good thing.
I invested in the laser/level tuning aids, Greg / MO wrote up a great review on these at this link:
http://www.huntingnet.com/forum/tm.aspx?m=1684829