Quiet Title how do you know if this has been done?

An 'Action to Quiet Title' is a court proceeding where the clouded ownership of a typically undisputed area of land is resolved by the court.

That decision is made by the judge as a finding which is recorded in the judicial record of the case.

Generally the successful party prepares a quit claim deed or similiar document and this document along with the court finding as an exhibit is recorded in the county recorders office,

Either way.. there is an official recording of the result and you can find it in the repective records.

Quiet title is complete once the deed has been recorded at the registry of deeds. The property can't be recorded if there is a broken chain of assignments

Usually both of the parties would know when it was taken to court, unless one of the parties did not show up or notice was not properly served. If it has been won, it would be recorded at the county (in the US), or whoever keeps land records where you live. A title search or title insurance (which does a title search) would reveal it if it was filed and won.

Is this for adverse possession or prescriptive easement? I assume someone filed or threatened to file quiet title against property you own, because if you were the one doing the filing, you would know the outcome.

You buy Title Insurance!