One way to see and use a diminished scale is as a combination of two dim7 chords.
As a starting point, one way to see and use one dim7 chord is as a dominant chord, and its "mount points" are on the third and seventh of the dominant seventh. For example if you have a G7, you take its third, B, and put a dim7 there. Or you could take the G# - a semitone above the root - and place your dim7 there. It's the same thing, because dim7 is completely symmetric.
This overlaying of a dim7 on a dominant seventh is quite standard jazz stuff. For example, G7 <=> Bdim7 (or Fdim7 or G#dim7 or Ddim7) ... But if you add Gdim7 as well, you get the G half-whole diminished scale.
- Gdim7 + G#dim7 = G half-whole diminished scale
- ... and it works as substitute for a G7 dominant chord.
It might be easier to remember, if you notice that the G half-whole diminished scale contains all of the nice colorful notes: root (G), major third (B), minor third (Bb), tritone (C#), seventh (F). And of course G# which is a colorful and bitterly melodic addition to a dominant. However it does not contain A, which sounds more like easy-listening, elevatory, mellow, soothing when added to a G. (My subjective opinion)
In addition to the dim7 chords, the half-whole diminished scale has ingredients for more weird/interesting/fun chords that can be used as a dominant. For example, G7 <=> E/G or C#/G.
Check out this incredible "E7" chord, which consists of various things taken from the E half-whole diminished scale:
It's like one of those ambiguous repeating patterns, "what do you see in this picture" ... well, depending on how you look at it, you might see Fdim7, Bb major, Bb13-9, E7+9, G7, Gdim7?
And because it's symmetric, that thing should work not only as an E7, but as a G7, Bb7 and C#7.