Firstly, navigate to Start, type dxdiag and open the application. Click the Sound tab, check your audio card model and download and install the latest drivers available from the developer's web page. After that, make sure that your computer sound volume is not turned to 0 and check the volume control located in the lower left corner of the YouTube video player:
If the problem is not solved, try turning up the volume of your installed video players, update your browser and install the latest version of Adobe Flash Player. Also, make sure that your security program or any other Firewall utility doesn't block third-party Flash content.