Of all the available tonal approaches, why use diminished? Because it's a great match for a raised-9 chord. Check the notation to get acquainted with the scale if you don't know it already. It's easier to memorize than most scales because it's built on a steady pattern of 1/2 step, whole step, 1/2 step, whole step.
Get the diminished scale into your "ears" before worrying about how to get it under your fingers. One very effective way to do that (with any scale, really) is to take just a few notes at a time. Choose a small subset of the diminished scale and improvise over the raised-9 chord.
The diminished scale also works beautifully with a blues scale. One way to bring them together is to start a line in the blues scale, and then bring in notes from the diminished. Listen to how those "diminished" notes break the boundaries of the blues sound resulting in very interesting lines for the listener.