I’m not sure what there is to say for MLAPI specifically. Your button will call a function when it’s pressed. In that function you can call a ServerRpc to run logic on the server.
The server has a copy of all network objects which exist. You can just access the NetworkVariables on the server object.
I figured out how to say what I want to do more clearly.
Lets say a player is attacking another player. I want to be do something like otherPlayer.TakeDamage() and have it work over the network. How do I do that?