Measure the area where the carpet transitions to the tile and make necessary cuts to fit the strip. Transition strips are either wood or metal and come in a variety of finishes. If the transition is wood, use a circular saw to cut it to size. If the transition is metal, use metal nippers to cut it down.
Use a carpet knife or a utility knife and trim the frayed carpet back. Do not over trim; just do the edges.
Take 1/4 to a 1/2 inch of the carpet and fold it under itself. Hold it into place for the next step.
Lay the transition strip over the folded edge of the carpet. The strip should extend onto the tile, but should be screwed in over the carpet and subflooring. Use a drill and insert the necessary amount of screws. Transitions are usually pre-drilled and will require between three and eight screws depending on the length of the transition.