How is this accomplished?

1.The Amulet of Mara can be bought from a priest named Maramal for 200 Gold,He can be found at either the Bee and the barb or the Temple of Mara in Riften.
2.Ask any marriageable Npc to marry you after you completed their quest.They will go to the temple of Mara in Riften, awaiting you. (The UESP wiki has a list of Npcs to marry)
3. There will be a ceremony, its pretty straight forward. (Be sure to talk to your spouse before they leave or else they will disappear from your game world forever).
4. Your spouse will move to any home you've purchased, you can tell them which one to move to if you have multiple homes.

Well one of my characters did all that Altair said and was snapped up by Iona before he even had a chance to think about who he wanted for a wife, or even what he was meant to do. The second character cannot get married no matter what she does, I am suspecting she has encountered some glitch.

It's better to not know about it, cause you'll regret the day after you are married. Next thing you'll be asking is how to get a divorce, and will start a plot to murder your spouse.

Well, aussie, I'm not sure what your first character did (or how drunk he was!), but you generally do get a chance to refuse or accept!

As for your second character, have they talked to Maramal about marriage yet? Even if you have an amulet (from him or anywhere else), if you haven't found out from him about how marriage works, you can't propose to anyone.

I never had them vanish. just always found them within 24hrs back at their old home doing stuff.

I would add if you want the Lovers Comfort bonus talk to them right after getting married. Tell them their home is fine and you will meet them there. Or if you married someone who can be a follower, then invite them to follow you and return to his or her home. Spend the night there and recieve the Lovers Comfort bonus. Now ask them to move to another home with you if you wish and you'll continue getting the bonus as long as your not a werewolf. For some reason if you ask your spouse to move to your home first you likely won't get the Lovers Comfort bonus.

Also like in real life, marry someone your going to be content with. I prefer to marry someone who can be taken as a follower to share adventures with. Since I'm on the PC I can set them to essential as well as forgiving should I hit them in battle (thanks to the Ultimate Follower Overhaul mod)

My curent character Salessi Darkwater is married to Farkas. Others are married to Lydia, Ysolda, Sylgja, Borghak the Steal Heart (female orc) and Camilla Valerius.

Well with the first character I had no idea a marriage proposal was going to be so quick! Went over to Honeyside to chat with Iona and see what it was all about, she accepted before I realised he had even proposed, and Braggen did not want to leave her at the alter so to speak. If there had been a wait and lets think about it option, or even a chance to change your mind before the ceremony Braggen would have chickened out.

Yes Aussie the second character got the amulet from Maramal, and had the discussion, wore it for ages trying to get some response, had her heart set on Argis over in Markarth. That was a long time ago though so I am pretty sure that amulet would have been swapped around by now. She gave up on marriage and thought maybe it was because she was a werewolf that was the problem, but she cannot even marry an ex werewolf. She might go see if she can buy another amulet and try Farkas again.

Thanks for the info.