To get married in Skyrim you will need to travel to Riften and find Maramal.
You can normally find Maramal in The Bee and Barb
tavern during the day or Temple of Mara
at night to sleep. If you cannot find him in either location you may have walked past him while he travels between locations.
Simply ask him about getting married. He will explain to you the process. Basically it goes like this.Step 1. Get an Amulet of Mara.
There are two ways of getting the Amulet of Mara. Both ways require you pay 200 gold. Your choices are...Step 2. Wear the Amulet of Mara in front of the one you want to be your significant other. Step 3. Return to Maramal and tell him you want to be married.
a. Purchase it from Maramal while talking to him. No quest, just move on to Step 2.
b. If you like quests, find Dinya Balu in the Temple of Mara to start the "The Book of Love" quest. Half way through the second love story that you assist in you will have to pay 200 gold for a poem. At the end of that story (roughly 2/3 of the way through the quest) you return to Dinya Balu where you receive the amulet. Do note that you have to complete this quest before you can use the amulet in Step 2.
He will tell you to be at the Temple of Mara at dawn.Step 4. Get married.
Enter the Temple of Mara and use the wait feature to progress time to after 7:00 AM. The game will auto move your character and start the 2 minute long ceremony. Step 5. Say yes!
That is it. You're married and the achievement should pop soon after the priest finishes officiating.