Properly installed landscape edging should not be subject to frost upheaval, which causes lifting or buckling. The best method to repair frost-upheaved landscaping is to dig out the edging and replace it. Consider replacing inexpensive landscape edging with a higher quality edging that is less prone to frost upheaval once it has been properly installed.
Dig up soil behind your edging with a spade and scoop shovel to reveal the entire back side of the edging.
Pry out landscaping stakes using a screw driver. Lower quality landscaping edging may not have been installed using stakes. Landscape edging that has been installed using steel stakes is not as subject to frost heave as edging that has simply been buried.
Smooth and re-grade the trench behind your edging with a rake. The landscape edging trench should be uniformly 6 inches deep. Cut any roots that you encounter with a pair of branch loppers.
Unroll high-quality commercial landscaping edging and place it along the edges of your bed. Edging is sold in 20 foot sections; connect sections together using 8-inch-long plastic connectors. Insert 4 inches of the connector into one edging piece and the other 4 inches into the other piece. Do not accidentally push all 8 inches of the connector into one piece of edging while trying to insert the other half into the second piece of edging; this is a common mistake made by landscapers. Cut the edging so that it fits around the bed using a utility knife.
Press the edging up against the side of the landscaping bed so the V-shaped curl at the bottom faces inward. The roll at the top of the edging should not sit above the soil line. Only the top 1/3 of the roll should be visible. Press the edging against the edge of the trench.
Insert the steel stakes into the bottom of the edging just above the V-shaped curl. Space the stakes so that there are only four stakes per 20 feet of edging. Align the stakes parallel with the ground and hammer them into the soil.
Pack soil down so that the edging is covered 1/3 of the way. Press the edging into the wall of the trench and stomp the soil to lodge it around the V-shaped curl at the bottom of the edging. Sprinkle soil into any gaps between the edging and the soil in front of it. Fill the trench behind the edging with soil completely. Water the soil to settle it in place and add more soil to fill in any gaps.