First log into Battle.net and add you game code for the game.
If you already have Wings of Liberty installed on your computer, you do not need to install Heart of the Swarm from the game disk. Instead, start up the StarCraft II launcher and allow it to optimize your game files and download any pending updates.
I tried to install from the disk but it was crazy slow.
I calculated 8 hours to finish based on the progress I waited for.
It installs both games, 15gb.
The optimizing thing on my machine took 10 minutes.
Then during the download you can play without getting it all.
The cut scenes would need to be streamed.
Then you can restart the DL after playing.