Mirroring in SQL Server 2012
Sorry for the previous useless response - skipped over the fact that you are setting up a mirror without a domain. You will need to use certificates for this. 

I found an article that might help you with that part. Check it out: http://mssqlnet.wordpress.com/2012/06/20/microsoft-sql-server-database-mirroring-in-a-workgroup-without-domain-with-certificate/