please tell me how I can obtain a "single certificate" for my upcoming marriage in Shenyang, China?

Hi, you need to sign a Affidavit of Single Status before a notary public, then get it certified by the Secretary of the State Office and attested by Chinese consulate. Please refer to http://houston.china-consulate.org/visa/english/marriage/jh.htm for detailed procedure. Make sure prepare its Chinese translation as well.