While consular officers at the Embassy are not authorized to perform marriages, they can assist U.S. citizens with the paperwork necessary for a legal marriage in Korea. A common misunderstanding is that you will be married at the Embassy; in fact, you and your fiancé/fiancée will be married under the laws of Korea. Marriage in Korea is a civil procedure, so a religious ceremony, while often more meaningful, does not create a legal marriage.

Here are the steps for getting married in Korea:

Bring all of ducuments listed above for each partner to the Embassy. Be sure to complete one copy of the Affidavit of Eligibility for Marriage and three copies of the Report and Certificate of Marriage.The Embassy will check all of your documents and norarize your Affidavit of Eligibility for Marriage. The total fee for the notarizations is $90 (no charge for military members).
Take the notarized copy of the Affidavit of Eligibility for Marriage along with three copies of the completed Report and Certificate of Marriage to your local ward office (Gu Cheong;구청; follow this link for a map to the Jongno office ) for approval and signature by a Korean government official. The ward office will keep one copy of the Report and Certificate of Marriage as a permanent record.
Finally, bring the two copies of the Report and Certificate of Marriage signed at the ward office back to the Embassy for authentication. The fee for this authentication is included in the $90 mentioned above.

That's it-- Congratulations! Please keep your marriage certificate in a safe place, along with your other important documents.

Please note that the above procedures at the Embassy and the ward office can normally be accomplished in an hour or two, so please plan accordingly. We are open from 9:00 - 11:30 and 1:30 - 3:30, and we are closed Wednesdays, and American and Korean holidays.

Source: http://seoul.usembassy.gov/wwwh2510.html#korean