If both PC's are on the same LAN (in the same house, using the same router), you can simply load a game on one PC, press Escape, then click the Open to LAN button. The 'Allow cheats' option will enable/disable commands, and you can set the default game mode. When ready click the Start LAN World button.
On the second PC, you can now go to 'Multiplayer' from the main menu, and you should be able to see the game running on the first PC - simply connect to it like you would any other server.
If you can't see it, then you may need to adjust Firewall settings on the 'host' PC.