I would suggest looking at the FamilySearch Wiki for the location of where the birth or marriage occurred. The Wiki will tell you when vital records started being recorded for an area to know if the record may exist and if it is available there may be links to search. Some indexed and some not. Them remember some records are just not on the internet and you may have to contact the state or county to request the records and that usually incurs a fee. Especially more recent records may not be available online.
What "Country" are you talking about?
And, just as importantly ...
What "Time period" are you talking about?