The Iridium Browser looks like a viable competitor to the Firefox-based component in TorBrowser. How would someone use Iridium with the Tor network?
Because Iridum is based on Chromium, instructions for using Chrome w/ Tor should work. Of course - just like using Chrome/Chromium with Tor is not recommended, I wouldn't recommend using Iridium with Tor either.
For one matter: you'll stand out as one of the very few people (only?) using Iridium over Tor. Your cross-domain and session unlinkability is gone.
Secondly, Maintaining Chromium forks is hard. Chromium has no Extended Support Release cycle. This introduces a difficult dependency cycle of [BugFix 1] -> [Major Release] -> [BugFix 2]. To get the second fix, you have to either accept the Major Release (including auditing the entire thing for proxy issues, fingerprinting, or cross-domain leakage) or backporting the BugFix. Other attempts at maintaining a secure fork of Chromium (Aviator) did not go well.