If your computer application doesn´t support AirPlay (no AirPlay icon) don't panic. There is an elegant solution to this problem. Try AirFoil from Roque Amoeba. AirFoil is a third-party "sound grabber" that grab audio from ALL applications on your Mac or PC and to forwards music to an AirPlay speaker your choice. Find information about AirFoil here. The cost of AirFoil is approx. USD 25 and you can buy it directly at the site.
When watching movies on your computer you should use the Airfoil Video Player (included in the license fee for AirFoil). This ensures that local video and remote audio always stays in sync. The player supports many video formats, including Flash and Silverlight web video, as well as basic DVD playback.
Note: As from Mac OS X Mountain Lion - AirFoil is not required anymore on the Mac platform (read more in the post above). Older Mac OS X versions still require AirFoil for system-wide AirPlay streaming.