What is DirectX ?
DirectX is collection of 2D and 3D-programming APIs developed by Microsoft. It's concidered to be a standard in game programming.
DirectX SDK is a software development kit for programmers to develope their own DirectX applications.
Where can I download DirectX 9 (for Win XP)?
DirectX 9c is available for download at Microsofts DirectX 9.0c download page
Where can I download DirectX SDK ?
DirectX SDK is available for download at Microsofts DirectX Software Development Kit page
What about DirectX 10 and 11 ?
There's more information about these in Microsofts DirectX page along with many other downloads. Check it out here
DirectX Programming resources:
DirectX programming tutorials
Drunken Hyena's DirectX9 tutorials
Lots of DirectX tutorials, some are commercial