Twist the old smoke detector and remove it from its bracket.
Unscrew the bracket for the old detector and remove it. Chances are that the new detector can be positioned to cover the old holes so no repair should need to be done to the ceiling.
Hold the bracket for the new detector on the ceiling so the new smoke detector will cover the holes from the old one. Mark where the holes are in the bracket by sticking a pencil through each one and marking the ceiling.
Drill holes in the ceiling where each mark is located.
Insert the plastic anchors that came with the new smoke detector into each of the holes. Make sure that the anchors are flush with the ceiling.
Fasten the new bracket in place by installing the screws through the bracket and into the anchors in the ceiling.
Fasten the new smoke detector onto the bracket after installing the battery.