http://skyrim-cover.blogspot.com/2011/09/marriage-broken-down-at-beginning-of.html
Once you've build up a relationship with one of the more than hundreds eligible bachelors, then no matter the gender and no matter the race, you can wear an amulet to signal that you're ready for the next step: Purgato... I mean marriage. I guess it's one of them cool Nord traditions; And we know that that'll turn out well! Just look at how great the dragon-worshipping went!
Once you've courted whomever you want to court and have become man and wife, man and man, or wife and wife, you're new partner does more than just hold that honorable title. Once a day, your spouse can cook you a meal to restore your strenght <3 If you have a house, your new love will move in with you, or if you so desire, he or she will become your companion, aiding you in your travels, be that by fighting at your side, or giving you some neat perks.