It was such an obvious oversight that I didn't realise you couldn't share your single-player world over the LAN games until recently. And now I'll never miss it: Mojang have just enabled in a weekly snapshot.
It has a few uses: showing off your amazing builds, asking for help with a tricky dungeon, or just playing the world with friends without worrying about paying for a server online. And the latest Minecraft weekly builds start up a server whenever you're playing a single-player game, so all the hard work is done: in the future, then the two forks merge, you'll be playing on a server no matter if you're online or off, and all you'll need to do to let others join you is tell the game to let them in. How do you do that? You'll need the latest snapshot. With that, here's a Minecraft snapshot guide to help you swap between the experimental and standard builds of Minecraft.
Set-up? Good. Now according to Mojang: "You can now use “/publish” to open your single-player game for LAN friends to join. This is still very much work in progress, so it lacks some necessary settings such as what game mode your friends will get, and if they should be able to use cheats or not. Also, the “/publish” command is temporary, you can’t even access it if you haven’t enabled cheats."
Gather friends and mine on!