It is becoming increasingly common that one party to the marriage is not a baptised Catholic. For a marriage to take place in the Catholic Church at least one party to the marriage should be a baptised Catholic.
The marriage papers are completed in the normal way, except instead of a Catholic baptismal certificate the non-Catholic party should provide an original copy of their baptismal certificate from their own denomination or if they are not baptised, an original copy of their civil birth certificate.
One of the local priests can help inform you of what is involved with this process.