OSX users: 1) FIRST DOWNLOAD THE MOD and install it into something like "~/Library/Application Support/Steam/SteamApps/Common/Portal 2" (the folder is hidden by default on OSX Lion, so go to Finder >> Go (menu bar) >> Go to Folder)... 2) Restart Steam, AND THEN 3) download and use this .app that acts as a shortcut... If you want to do it the manual (and less obtrusive) way via Terminal and making a symlink, read more...
There's another way to do it, if you don't like that way...
On OSX, the problem is that Steam doesn't execute (though it properly scans, or something) from /sourcemods/ or something, so you have to make a symlink to the Portal 2 directory.
1) Keep the extracted /levelwithme/ mod in Steam/SteamApps/sourcemods/ instead.
2) In Terminal, execute:
~/Library/"Application Support/Steam"/steamapps/common/"portal 2"/ ln -s ../../sourcemods/levelwithme
3) Restart Steam.
4) Then in the Steam games list, right-click on "Level With Me" >> Properties >> Set Launch Options.
5) Set launch options to -game levelwithme press OK and now you should be able to start the mod from Steam while keeping your core Portal 2 folder uncluttered.