A result of Shelah about the nonstationary ideal

Try also Chapter XVI of "Proper and Improper Forcing" (entitled "Large ideals on $\aleph_1$ from smaller cardinals"). It's hard to tell exactly what's in there, but he does say in the chapter he will "keep old promises from 84-85 mentioned in [Sh:253]", where [Sh:253] is the paper Michael mentions, and he does claim to be replacing certain hypotheses used earlier by the assumption "$\lambda$ is a Woodin cardinal".

I have a writeup Shelah's proof of the consistency of "NS is saturated" relative to "there is a Woodin cardinal" on my web page: https://ivv5hpp.uni-muenster.de/u/rds/sat_ideal_better_version.pdf

Jech (in the Chapter "Stationary Sets", from the Handbook of Set Theory) lists the reference as

Saharon Shelah. Iterated forcing and normal ideals on $\omega_1$. Israel Journal of Mathematics, 60(3):345–380, 1987.