After the wedding ceremony is over, the marriage license must be signed and completed by the couple and officiant in the presence of any required witnesses. Following that the marriage license must be returned to its issuance office.
When the couple files for the marriage license they typically receive specific instructions on when and how it needs to be returned. Generally, the completed marriage license needs to be returned its issuance office immediately after (or within a few days of) the ceremony.
Check out our state marriage license infopage for state specific information on marriage licenses, including the waiting period, expiration, and return deadlines.