Unscrew the two screws holding the trip-lever faceplate to the overflow. Make sure to use a properly fitting screwdriver to avoid stripping the screws.
Once you have the screws removed, lift the faceplate and assembly from the overflow. Pull the whole assembly out only a few inches, there's no need to pull the whole mechanism out from the hole.
Tip the faceplate forward until you can see the backside clearly. You should be able to see a cotter pin holding the assembly onto the faceplate.
Remove the cotter pin from the linkage arm. Slide the faceplate off.
Take the faceplate to the hardware store and buy a comparable model. Reinstall the faceplate by following the same steps backward.