how do you invite a friend on minecraft into your world?

[Kelee]

like not just a server but your own little world place

[Jakob]

Friends cannot join your world if it is not connected to a server

[ladenzor]

That only works if you are on the same network. On the pause menu select "Open to LAN." The game will show up in the multiplayer list of anyone else on your network. You can make this work over the internet with Hamachi, however, but you and your friend both need to have it installed. See here for help with Hamachi:
http://www.ehow.com/how_10012956_hamachi-minecraft.html