I get an error message every time I try to install Portal 2 via Steam

Solution 1:

Apparently that message only means the Steam servers are busy, it worked now.

From the Steam website:

Incomplete Installation (10)

Steam servers are busy. Please try again later.

Solution 2:

When I got this, it was because my computer had gone into hibernation during the download. A Portal 2 update came a few seconds later, fixing the problem. Verifying the game cache was unnecessary.