Always, when you run Minetest without connecting to any server address (leaving the address blank), you actually run a server. Just find out your IP using for example http://www.whatismyip.com/, start up the game and ask your friend to connect to that address.
Connecting to your server might fail because of the port being blocked by a firewall or a NAT router. You need to have the UDP port 30000 (or whatever port you are using) open to the outside world to allow others to connect.
For Linux users: If you use wireless internet and nobody can connect to your server, your ip address may be different from what's shown at whatsmyip.org. In this case, log in to a shell and run the command “ifconfig”. It shows you all your network cards and their current IP adresses.
It is also possible to run a dedicated server.
minetest.exe --server --dstream-on-stderr
Or copy it from here. Then just launch runserver.bat.
minetest.exe --server --gameid mesetint
IMPORTANT: Never run two servers or a server and a local game in such a way that they access the same world simultaneously through the file system. This will likely corrupt your world. There is no lock files or anything that would prevent this.
TO BE SAFE, never run minetest as two instances from the same directory; extract a new copy from the zip for a separate client if you run a server which accesses your world.