Lay the frame and picture on its face on a flat surface to expose the back. Look for the catches that keep the back of the frame in place. These are small metal pieces, and extend from the frame over the back of the picture. They might slide, rotate or screw into the frame. While small picture frames have only two to four catches, larger ones can have two to four catches on each side.
Use a screwdriver to unscrew catches that have screws, then slide the screwdriver or other small tool under the catches to move them. Slide them as far toward the frame as you can, so that the back of the frame comes loose. Lift the back of the picture out of the frame.
Leave the matting where it is, as it fits the frame best that way. Most mattes are cut for the frame as rectangles, squares or other shapes, and won't fit when rotated. Lift the artwork off the matte and rotate that per your personal tastes. Turn the artwork 180 degrees to flip the frame, or turn it to the side to offer a different fit and vantage point. Check the artwork before you put the back on again, if you question whether the placement is straight. Hold the artwork with one hand and turn the frame over, then adjust the art as you watch. When you reach the placement you want, turn the frame back over to expose the back again.
Lay the back of the frame back on the artwork, without moving the artwork underneath, and move the catches back to secure the piece. If your catches screw, screw them back in carefully to avoid displacing the artwork.