The new MacBook Airs don’t have Flash installed by default so this is a tl:dr summary of those two articles so you don’t have to download and install the system-wide Flash player.
Many sites, such as YouTube, provide content in an alternative format for devices that do not have Flash installed. Get access to this from Safari by turning on the ‘Develop’ menu (Preferences | Advanced) and change the User Agent to ‘Mobile Safari 3.2.2 iPad’. This works per tab|window so doesn’t change the display in what you already have open.
If this still doesn’t work (I’m looking at you iPlayer) then you can use Google’s Chrome browser, which comes with its own Flash plug-in.