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a local area network minecraft server allows you to play minecraft with a friend without an online connection, though your friend needs to be with you (in real life). simple as that. Besides if you looked for this guide you must have a small understanding of local area network connections, if not...find a guide for that as well.
Anyway straight to it, i use a LAN server with friends because i dont seem to get lag as much or more often as were just connecting through a router. i couldnt find any guides online so after screwing around i found out how:
Step one: Get all the stuff you need- have the game, the server file, ETC. its self explanatory.
Step two: after you download the server file off minecraft.net , run it as a .exe file to create a server file(which is calle "server.Properties"), for me it goes to the desktop, but i've been told it can come up elsewhere. open it as a .txt and it should look like this:
#Minecraft server properties
#Sun Jan 09 11:00:38 AST 2011
level-name=world
hellworld=false
spawn-monsters=true
online-mode=true
spawn-animals=true
max-players=20
server-ip=
pvp=true
server-port=25565
the file uses True and false as "yes and no". you wont need to bother with server ip and port but you can change whether monsters spawn, animals, and most importantly online mode.
Note: hellworld set to true seems to make everyone spawn in hellworld, which isnt fun when you dont have anything on you.
The most important thing to do here is set online mode to false. and after you done configuring its should look like this:
#Minecraft server properties
#Sun Jan 09 11:00:38 AST 2011
level-name=Tablecraft LAN guide
hellworld=false
spawn-monsters=true
online-mode=false
spawn-animals=true
max-players=20
server-ip=
pvp=false
server-port=25565
i usually set pvp off but thats all preference. after you have that setup you can save and close it. Change the file BACK to a .Properties file so the server reads it. Now make sure you restart your server and "VIOLA!!" your lan server is online.
Step 3- Connecting to your server
Connecting to your own server is simple, its getting your buddies on it that gets difficult.
to get on your own server go to multiplayer (in the game duh!) and type in "Localhost" and you should get in quickly. this is for the person HOSTING the server not everyone. for everyone else, they will need to connect to your ip. who-ever is hosting the server will need to open the start menu and go to Programs-->Accesories-->Command prompt and click it. if it is not there you can run it by clicking RUN and typing "CMD.Exe" and if RUN is not there do a file search for it there should be a file for it somewhere on your computer.
When command prompt opens type in : IPCONFIG
it should generate more text in that text you will find an IPv4 address or IP address, it usually looks like "192.###.#.##" with the number signs as numbers, your friends will need to type this in when their minecraft asks what to connect to. in normal situations they will connect to you normally. when all your friends connect, commence minecrafting.
Enjoy the good times that lie ahead of you.
Extra server notes: the server self saves, which is handy and it saves to a folder called whatever your server name is where your server properties file was, i suggest not fooling with that or you will error whenever you login to your server if you messed it up.
Extra server note#2: the server saves usernames, so if you login as someone else on your computer who was previously logged on you will resume where they left off along with all they were carrying.
Guide brought to you by Tablecraft, minecrafts funnest. 
