Dajukebox has several ways of using your soundcard. Under windows XP both DirectX as ASIO output are supported. Under Windows Vista and Windows 7 DirectX, WASAPI, both shared and exclusive modes and ASIO are supported. The output to use really depends on your usage of Dajukebox. WASAPI and ASIO are low latency direct accessing your soundcard. DirectX uses the sessions of your windows audio system.
For ASIO drivers you will need to check with your soundcard manufactorer. If you wish to use ASIO capabilites you can use ASIO4All to install a general ASIO driver. ASIO4All can be downloaded from http://www.asio4all.com/. On their website there is also tons of information and links on ASIO, how it works and what problems you might encounter.
For the WASAPI information we recommend you read http://msdn.microsoft.com/en-us/library/windows/desktop/dd371455(v=vs.85).aspx. It gives you a good idea on how WASAPI works. In our setup we found that shared mode only works if if there is already an application running using WASAPI (for instance windows media player). If there is no app running then you need to use exclusive mode.