If someone was married in a civil or Protestant ceremony or otherwise not following the rules of the Church (e.g. if there was an impediment) there are two ways to regularize the situation. The usual is a convalidation, in which the couple take their vows again witnessed by a priest or deacon.  

Radical sanation ("sanatio in radice" for "healing in the root"), a retroactive validation and retroactive application of any dispensations, without renewal of consent, is also available and more appropriate for certain situations. As I understand it--and I'm not a canon lawyer--if there is no impediment a convalidation can be done by the parish priest but a radical sanation is from the bishop and reviewed by the diocesan tribunal.

These are often done when one or both of the spouses returns to the Church and wants to present himself or herself for Communion again. A marriage between two non-Christians is presumed valid so it is not necessary for conversion.