Assemble the picture frame either before or after you do the carving, depending on how elaborate it is and where it is located on the frame. If you will be carving the corner joints directly, you will need to assemble the frame first.
Strengthen the corner joints of the frame by running the corners across a table saw or by notching them with a handsaw and gluing in a shim that extends across the joint and into the two sides of the frame. Clamp the frame together and allow it to dry thoroughly before carving it.
Sharpen your chisels thoroughly. Trying to carve with dull chisels is an exercise in futility.
Draw the design you will be carving onto the surface of the frame with a sharp pencil.
Begin carving with a straight chisel, incising the defining features of the carving and taking out a small sliver of wood along the main lines.
Bring out the three-dimensional forms of the different features of the carving by using the appropriately shaped chisels for each shape. Be particularly careful carving around the corner joints, and don't carve so deeply that you expose the shim that is holding the corners together.
Finish sand the carving with fine sandpaper of 220 grit or finer.