1. Navigate to an existing starcraft2 install directory on your home computer, laptop, etc.
2. Simply copy the contents of the folder onto a thumbdrive, dvd, or whatever else you feel like using.
Note: To save space, you do NOT need to copy the campaign folder (2+ gigs) if you are just going to be using sc2 for multiplayer/custom games. There may be other files/folders you can omit from copying, but that is all I've tested. Make sure you include the Starcraft II Editor.exe.
3. On the computer with restricted access, simply copy the files into a directory on the harddrive i.e C:/starcraft2.
Note: At this point you can try to run Starcraft II.exe directly, with your fingers crossed. Unfortunately, it gave me an error message:
"Launcher is unable to restart with administrator privileges. Please enable UAC or run Launcher from a user account that has Administrator access."
4. Launch Starcraft II Editor.exe. It will prompt you to log into your battle.net account with a small pop-up window.
5. Log into b.net. It should now load a blank map.
6. Press Ctrl-F9 or the run sc2 icon to "test" your blank map in sc2. Sc2 should now launch, load the blank map, and go straight to a "tied" menu screen.
7. Click quit on the menu screen. It should now take you to the default SC2 menu screen.
Note: I've only tested it once, going from a very beefy x64 win7 computer to a much more modest 32bit XP school computer. If it works in this case, I imagine it should work between most machines, assuming their capable of running SC2 at all. However, there may be software dependencies such as Direct X which if not installed could prevent you from playing.
Good luck!