I hope I've come to the right place

I am due to get married to my non-EU/EEA fiance who does did NOT require a visa to come to Ireland as a tourist but does require permission to reside in the state for more than 90 days.
My fiance has been here as a student throughout 2019 (we've known each other for years previously) although in 2019 we got engaged and will be married in the coming days in Dublin.
I have two queries about what steps we should take next after we get married and are officially a married couple.
- Online I've seen many different scenarios as to what people have done after they've got married abroad. We however will be marrying in Dublin, and I am curious as to what procedures we should follow once we are officially married? As my fiance has already been here legally as a student should we need to go into the Immigration Office/INIS to show our marriage documentation so my fiance (soon-to-be) spouse can be documented? Or is this done online? I've seen conflicting information online. My fiance has already been in the country throughout 2019 and did not arrive here on a short-stay visa to get married. She has been here on a student-visa which recently expired.
Any assistance would be greatly appreciated.