How to play minecraft locally?

I'm not very good with a mac. I know the basics and thats it. I'm trying to play minecraft with my brother on a local Wi-Fi network. We have two separate computers. One is a PC and the other is a mac. I have purchased minecraft legally and i just want to play multiplayer on a local Wi-Fi network, is there a way to do this?

I have just bought Minecraft too- Christmas 2013 if fact! I'm still a newbie but I know this one- here goes:
NEEDS 2 SEPARATE ACCOUNTS ON TWO SEPARATE COMPUTERS
1) Create/Open a server on one computer
2) Press Esc to open up the options menu
3) Press Open to LAN. All this does is quickly create an online server.
4) Other friend to Open Minecraft and press Multiplayer
5) If you are playing on the same internet connection (which you are by the looks of things) the brother should see your world beneath/on top of the Scanning the Local Server etc.etc.etc. Click it and you will be in the same world as him!
One problem- if the person who created the world closes it, you have to start again!