Changing from a string peep to the Anchor Sight is best done using the following method:

If you have used a peep sight for a long time you have been forced to established your anchor point by leaning over the string. The key to shooting in a hunting environment is having an anchor point that gives you the most consistency, feels right and is torque free. Remember, the purpose of the anchor point is to position ones eye in exactly the same spot every time while not putting torque on the bow. For many shooters, the anchor point dictated by a string peep is not a good one for holding the bow without torque.

This will help you find a good natural anchor point:
Without using the Anchor sight or peep, install the Anchor sight frame under your front sight frame, then move your pin(s) out 1/8 inch to compensate for the frame thickness, sight in your front pins on a target, at say 10 yards, using only the anchor point you come back to naturally. Shoot until you have established a grouping and feel you have found your natural anchor point. Get your groups on the bullseye of the target by moving your front pin. Now, sight the Anchor sight to your eye at that new anchor point. When you are comfortable with the alignment start shooting using the Anchor Sight. More likely than not you will see your groupings go slightly off target because you did not get the Anchor sight perfectly aligned to your new anchor point. To do this you simply move the arrow group on the bullseye by using the Micro adjustments.
If you are right handed... and the group is off to the left of the bulleye, you turn the side (horizontal) Micro screw clockwise until the group moves on target. If you are low, turn the Vertical Micro clockwise and your arrow should go up. When the arrows group on the bullseye, you have gotten back to the exact anchor point (eye position) you had chosen. Once you have found a good anchor point, you can sight-in using your front pins just like you did with the peep sight.