Before you can actually meet somebody, you'll need to go to the Temple of Mara in Riften and inform yourself about marriage at the local priest, Maramal. On rare ocassions, he can be found in the Bee and Barb tavern, also in Riften, but since he lives in the temple, that is your best bet to find him.
After asking about the temple and informing yourself about marriage, you will be able to buy a necklace for 200 gold that shows you're 'available'.
Buy and wear the necklace, and find yourself a partner. Your own race and gender does not impact the choices you can make.
A full list with name, race, gender, occupation and required quest/action can be found here:http://www.realsg.com/2011/11/guide-skyrim-marriage-how-to-a...
All credit goes to Anthony Accinelli who created the list.
After choosing your partner, head back to the temple and arrange your wedding with Maramal. Wait for a day, but NOT inside the temple, and re-enter to attend your marriage.
The achievement will unlock after saying 'I do'.