1-Open firefox and type about:plugins in the address bar,If you found it in list of plugins then u dont have to install it ,but if there is no adobe flash player in the list you have to install it .
2-Open youtube and try to play avideo as the screen below you will observe that the video does not work and ask you to install the latest version of adobe flash player , click on insall missing plugins .
Click on find out more plugins or manually find missing plugins
It will open a new page shows list of Add-ons for firefox among them adobe flash player, click on download now button.
It will open the page of get Adobe Flash Player, Click on different operating system or browser?
Select Linux from slect operating system menu .and select flash player 10.3 for ubuntu (apt) from slect version menu , and then click on download now button .
Launch Application window will appear, Mark on Ubuntu Software Center ,then click ok .
Ubuntu Software center window will open ,and show Adobe Flash plugins 10 , click on install button to install it .
Type your password and click on Authenticate button .
Adobe Flash Plugin 10 is being installed ......
When it over restart firefox and play youtube video to be sure .
Now have fun with youtube after installing flash player .