If you make a humanoid take damage using a localscript then the damage won’t replicate (show) for other players, so you need to do that from the server. In order to let the server know when you want to deal damage you should use RemoteEvent | Roblox Creator Documentation. To keep things simple you can just send the humanoid they wish to damage.
To know what damage should be dealt you should have Instance Attributes | Roblox Creator Documentation which stores the damage value in order to prevent exploiters from dealing insta-kill damage. You should also implement sanity checks so they cannot damage people from across the map.