How does it work and how does one do it? Can any priest of any cult perform the rights? Is non sigmarite marriage even recognised in the empire? Does Sigmar have the marriage monopoly? Your thoughts...

Firstly I have no idea what is canon on this.

However, if you assume the Empire period to be roughly 16 hundreds century Germany. Then marriage was primarily a secular affair. Nuptial blessing were popular but not legally required. The requirement for church weddings came later I believe - which was driven by the desire to have a marriage registry. Essentially legislation to limit bigamy.

Basically any promise of marriage followed by sex could be a legal marriage. A publically stated promise followed by sex should be legally enforcable.

In second editon Warhammer book, "Heir of Sigmar", there were details on marriage ceremonies.

Sadly, I don't remember them.