Minecraft Play from 2 different computers in the same house

Solution 1:

First you will need to purchase a second Minecraft account to play with and install Minecraft on your downstairs computer.

Once you've got Minecraft and you can log in, one of you can open a world and press ESC to bring up the menu:

Click the Open to LAN option. A new screen will come up allowing you to select the game options you want to use, and then select Start LAN World to open the LAN server.

The other player should be able to connect at the bottom of the list on the Multiplayer screen:

Solution 2:

Alright took a minute to do this.

Have yourself or your son create a world. Enter that world, moment you enter hit "esc" should see a button "Open to LAN" click it. Will give you a couple toggle options, click "Start LAN world" will load for a second then give you an IP address that you may or may not need.

Next have the other person go into Multiplayer should automatically start scanning for local games, meaning the game you just opened to LAN. Once you see the server appear just join it. If it doesn't show up just go to "Direct Connect" and type in the IP address that your game gave you previously.

Pretty sure you need 2 copies of Minecraft for this.