How do you play multiplayer on a video game locally from one PC on two or more PCs

You would have to have a copy of the game installed on each PC. The game would need to be LAN capable, and most newer games will not allow LAN games unless you have bought separate copies of the game.
In any game capable of LAN multiplayer, there will be an option in a multiplayer menu to play across a LAN or Local Connection, you need to have each computer networked together and able to see each other across the network.
There are so many things that could go wrong that in order to make this kind of thing work you usually need to have at least one technical person helping you with the setup.