Me and you couldn't play together over a LAN russ, if you wanted to play with goosey baby, you couldn't play over a LAN, we would have to play over the internet because the three of us are in different locations.
If me and goose came to your house though and we all connected to your home network, all on your same router, we could play over a LAN, and that would be the same if we went to goose or you came to me.
When people say they are going to a LAN party or they were playing over a LAN or anything similar, they mean that they were around at another person's house or they were at an event playing with others. By an event I mean things such as Dreamhack or insomnia (will explain in a bit).
You can get a program called Hamachi though which simulates a LAN over the net, so me, you and goose could connect to the same Hamachi server, one of us set up a LAN server and we could all connect, even though we aren't physically on the same local network.
For how you go about setting one up, it differs from game to game. If a game has LAN support, generally there will be an option to list LAN servers if you go into the multiplayer area of a game, and on there it will say something along the lines of host a server or similar.
About the events:
Dreamhack - it is the world's largest computer event that isn't just gaming, it is everything to do with computers. It's in Sweden, and like most other events, you pay a fee to enter or extra to actually participate (anybody can). They do all sorts, there is competitive gaming, casual gaming, people programming, people making music, and everything else. You can find out more about it here:
http://www.dreamhack.se/DHS11/event-information/what-is-dreamhack/
insomnia is a gaming event set up by Multiplay (the people who host servers. We've got our Minecraft and TS server with em) which is called i## where ## is the event number, so this current one is i42 as it is the 42nd one they have done.
http://iseries.multiplay.co.uk/
both of these are examples of large LAN events where everyone gets together and can play together, or do things together on their computer without using the internet to do it