What is the correct way to use the Zerostat?

An old trick is to point the Zerostat away while pulling the lever, then towards the brush when releasing. This gives the record brush a neg. charge and is quite effective for collecting debris. Best results occur by treating the lp while off the platter. Audphile's suggestion for grounding is good, try touching the TT's spindle with one finger and a grounded unit (amp's faceplate?) with another finger to neutralize system static.

...and don't do something foolish like press your finger on the tip of the gun to test if it's working, it hurts like hell.

Release the trigger slowly. Don't just let go. I take up to 5 to 8 seconds to completely released the trigger. You can hear it.

Can it damage cartridges?

Audphile, I haven't read every single post that followed on to your first one, but if you use the (old style) Audioquest brush AFTER you use the Zerostat, you are likely putting static charge back on the LP after you neutralized it with the Zerostat, whether you moisten your fingers or not, because the old Audioquest brush provides no electrical continuity between the bristles and the handle.  Zerostat treatment should come last. (There IS a new Audioquest brush that is grounded via the body of the user, by holding its handle during use, thus perhaps it does not create a static charge on the LP. I don't know when the new version of the brush came on the market, but I think it is quite recent.)

I don't argue with the notion that the LP should be sitting still, not rotating, but I do not understand why that would be the case.