Start with contacting the church. Perhaps search the FamilySearch Wiki for the church or the location of the church to see if FamilySearch even has records for the church. They do not have everything.
Cindy gave you some great suggestions! If the church is still in existence, they will often share records with you. You can reach out directly to the church.
When you search in the FamilySearch Catalog,
I would look first by location - the state. You can search for church records in the listings. It might also be a good idea to search by the name of the church as a subject too.