Summarize the following:
Minecraft allows you to easily start multiplayer games if you are all connected to the same local network.  If you're at home, chances are all of your computers are connected to one network. Things may be a little more complicated in a school or work environment. Click here for details on configuring a network. You can use a VPN (Virtual Private Network) to connect multiple remote computers together on one network. This can be great for getting friends from different places together without having to create a server. Click here for details on setting up a VPN for you and your friends. In order to connect to the game, all players must be playing the same version of Minecraft. Decide which computer will be starting the game, and then use the profile editor on all the computers to set the version to match.  Start the Minecraft Launcher and click the Edit Profile button. Select the correct version from the "Use version" drop-down menu. This computer will be referred to as the "host", and should probably be whichever computer is most powerful. Load up one of your worlds in single-player mode on the host. Once the world has loaded, you can open the game up to anyone on your local network through the Pause menu. This will begin the process for setting up the network game, and a new menu will appear. You can choose between Survival, Adventure, and Creative modes, as well as toggle cheat codes on or off. Click the buttons to switch between options. The other computers on your network will now be able to connect to your game. Make sure that the computer is connected to the network, and that it is running the same version of Minecraft that the host computer is running. Minecraft will scan your network for any active games. The host computer Minecraft game should appear on the list. If the game doesn't appear, click the Direct Connect button and then enter the local IP address for the host computer. Click here for details on finding the IP address of the host. Your display should say LAN World above the game name. After selecting and joining, the world will load and you can begin playing. Once all of the players have joined, they may find themselves far away from the host, especially if the host has done a lot of exploring in the game already. The host can teleport each of the players so that they can all play together.  On the host computer, press T to open the chat window, and then type /tp PlayerName HostName and press Enter. This will teleport the player named PlayerName to the host. Repeat this for all of the players. Make sure each of the players sleeps in a bed in your new location. This will ensure that they spawn there if they die.

Summary:
Ensure that all of the computers are connected to the same local network. Ensure all players are running the same version of Minecraft. Start a game on one of the computers. Press the Escape key to open the Pause menu. Click Open to LAN. Decide on your multiplayer game settings. Click Start LAN World to begin the multiplayer session. Start Minecraft on the second computer. Click the Multiplayer button on the Minecraft main menu. Select the game and click Join Server. Have the host teleport all of the players together.