You and a mate can play using a single player world over a LAN or using a multiplayer world using server.
Single player LAN
- One of you start playing a single player world in the setting you both want.
- Set the game option to make the world "Open to LAN"
- Have the other player chose the LAN world through the multiplayer menu of worlds.
- The first player must keep playing to keep the LAN link active. If they leave the world, the LAN connection will shutdown.
- One player needs to run a Minecraft server program. Mojang provide one from the same source as Minecraft. Another option is Craftbukkit ( Get Bukkit ) ,which is what we use for our Frontier and Sanctuary worlds because it is easy to add Bukkit plugins.
- List both you and your friend in the white-list and activate the white-list in the server.properties.
- Change any further aspects of the server.properties to define the type of setting you want.
- Make the port that the server uses accessible to the net. Hamachi is one option to this. Using a commercial server host is another.
- The server will run without anyone actually playing on it.
Hope that helps