The standard Screenly Player is Raspberry Pi based, so reinstalling ScreenlyOS on one is the same job as installing it on any Raspberry Pi. The image is a public download and the steps are identical.
Follow Write the image.
You will need to open the case to reach the microSD card. Everything after that is the standard process: write the image, put the card back, power the player on, and pair the code it shows.
Note
You should not need to do this to get a new player working. Players ship with ScreenlyOS installed, and the software updates itself once it is online.
If the player will not start at all after a reinstall, see Flashing problems.