Unpack the flexible transition strip from its packaging. Uncoil it as best you can. If it continues to wrap back around itself too tightly, aim a hair dryer on the highest setting at the strip to help it uncoil.
Unhook the carpet's edge from the tack strips installed along the curve and peel it back. Lay the flexible transition strip between the other flooring type and the tack strips. Work your way along the curve. Keep pressing the transition strip tightly against the subfloor underneath the other flooring type.
Drive staples through the flexible transition strip and into the plywood subfloor with a staple gun. Work your way along the entire curve. Use as many staples as necessary to hold the flexible transition strip tight to the subfloor. A sharp curve will require more staples.
Roll the carpet back over the tack strips. Set a knee kicker about 1 inch from the transition strip. Hit the knee kicker with your knee to pull the carpet forward and hook it back onto the tack strips along the curve.
Use a 1/2-inch putty knife to push the carpet's edge down between the flexible transition strip and the tack strips.