All you need to do to play SMP is click on the "Multiplayer" button and enter a server IP number or URL.
If you're talking about hosting a server of your own, that's a different story, and your best bet is probably to get one of your more computer-savvy friends to be the host. If you're all basically clueless, you might just want to get together and play on one of the many existing servers listed here.
The only way to have a 'private map' (without the quotes, since it'd be an actual, um, private map) is to host your own server. I dunno about LAN; I assume it'd work (you'd just be entering a 192.168.0.x IP to connect, I guess?) but I've never tried, so hopefully someone who has can either confirm or deny.
They all work. The question still is if you've bought the game, if you're looking for a server or if you're wanting to host one.
The local loopback address only lets you connect to yourself. Giving that to your friends, even if you're all on a LAN, is just going to cause trouble, as you'll each be attempting to connect to yourself and not the server.
If you have a "standard" home router, you'll most likely have a 192.168.1.X address. Open a command prompt/terminal and type (windows) ipconfig to find out what your address actually is. Not sure of the Mac command, and it's ifconfig in the linux distros I've used (but I somehow doubt you're using linux).
Yep. It is the server map, so it will be saved, as well as everything in your inventory and chests. So just make sure you know your computers LAN IP so you can tell your friends to log into that one. They have to be connected to the same router as you though, as you aren't port forwarding. (Port forwarding is a pain in the ass, don't use it)
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No, then nether should be the underwhere, then we have the overthere, the downbelowthere, then the whoops-made-a-wrongturn-ther. - Hal9000