Hi there! I have a mac, so I cannot help you if you have Windows, Linux, or any other OS than Mac OSX.
First, find the library folder in your system. It might be hidden, but no worries. There are plenty of tutorials on YouTube about it.
Next, find and click the Application Support folder. It should bring you to a list of apps and stuff like that.
Then, find minecraft. Click on it. This is the folder containing all of the things the game uses.
Find the folder that says saves. These are your worlds. Find the desired world and move it from his computer to your computer. Make sure that you put it in saves, in minecraft, in Application Support, in Library.
Start Minecraft, and it should be there!
Sorry, I have not tested it, but based on my current understanding, it should work between 2 computers using the OS X operating system.
Let me know if I helped, and how I could improve. This is my 1st post here, after all.
