In order to marry someone, go to Riftin (far right side of Skyrim) and head to the Temple of Mara. You can purchase an Amulet of Mara there for 200 gold. Then, wear it around, and someone will eventually tell you they're interested in you. It's more likely if you do something for the person before hand.
After the marriage, you can either tell your spouse to come live in your house, or go live in theirs (if they have one). You can switch houses later, if you want.