You may have had problems playing flash videos recently and have been presented with a message saying that your player is out of date, and that you can either play (just this time) or upgrade. Clicking on upgrade takes you to the adobe website -- downloading the file is easy enough, but then what?
Well, here's how to upgrade.
Download the file install_flash_player_11_linux.x86_64.tar.gz
extract the libflashplayer.so file from the root of the compressed file
Figure out what files to replace:
So, in the directory where you put your new libflashplayer.so
sudo cp libflashplayer.so usr/lib/chromium-browser/plugins/libflashplayer.so
sudo cp libflashplayer.so /usr/lib/flashplugin-nonfree/libflashplayer.so
Restart your browser, and you should be good to go.