Once you are satisfied that the marriage license is valid and all the information on the license is correct, complete the fields relevant to you as the officiant and sign the license along with any required witnesses.
This might seem obvious, but it is important that all the information is presented correctly on the document. You can either do this by checking the details against the couples and any witnesses' drivers licenses, or by asking them to verify that their names are printed correctly. Changing these details after the fact can be a complicated process.
For more information on how to fill out the marriage license as the wedding officiant, check out How to Fill Out a Marriage License.