Those tiles are like tongue & groove flooring. Each tile has t&g that lock together and tongue side is stapled to the wood frame. Check youtube videos on how to install/repair those tiles. They are usually 12x12" and should be same t&g. Take one to the store and compare, even fit them together to confirm that t&g fit and the faces are even.
Remove the damaged/hanging tiles. Remove the staples or gently pull the tile away from the staples. Don't pull too much. You can damage the tongue on adjoining tile. Just pull away until the tile is off the staple then try to pull away horizontally away from the adjoining tile. The tile that is not damaged but "loose" can be put back with new staples.
When stapling, put the stapler against the edge of the tile and try to be gentle. Don't break the tongue with the stapler.
Get extra and learn on the job.
At the end, you run out of tongue. This is usually the end of the ceiling. You face nail the edge and cover with a trim or fill the hole with filler or caulk. My parents' bsmt is such ceiling tiles but surface texture is different. I used modern tiles to repair and caulk the seams to make it as "seamless" as possible.
Remove the damaged/hanging tiles. Remove the staples or gently pull the tile away from the staples. Don't pull too much. You can damage the tongue on adjoining tile. Just pull away until the tile is off the staple then try to pull away horizontally away from the adjoining tile. The tile that is not damaged but "loose" can be put back with new staples.
When stapling, put the stapler against the edge of the tile and try to be gentle. Don't break the tongue with the stapler.
Get extra and learn on the job.
At the end, you run out of tongue. This is usually the end of the ceiling. You face nail the edge and cover with a trim or fill the hole with filler or caulk. My parents' bsmt is such ceiling tiles but surface texture is different. I used modern tiles to repair and caulk the seams to make it as "seamless" as possible.
