Having recently painted some Giger art on my tank I can, at least, tell you how I did it.
This shows what I was aiming at, and my first attempt:
And this is annotated with the stages I used to achieve it on the tank:
Beyond that, I can't really help with "how" to paint like him. I was only copying one of his pieces. It is very hard to match the level of detail he adds to his work, especially in scale, but it is possible to give a representation of it.
Can't help with airbrush work, I don't have one.
Good luck.