I previously wrote on this topic here.
Obviously, this is a topic that is close to my heart as I was finally able to get my fiance to play with me and stop hating the game so much.
Just as this is a very positive experience, prepare for the rough parts. Your significant other may or may not have played another MMO previously. Mine never had. The extent of her gaming was Super Mario World and Goldeneye. Social interaction was a very new experience to her. It is your job to get her/him acclimated to their new environment.
Step 1, Don't force social interaction on them: If they have agreed to play with you, then they are doing it for you. They may or may not get the social aspect of the game. Don't force them to play in groups. They may feel like a 5th wheel, which can be discouraging. Have you ever been to dinner with a friend and his/her significant other.....it is kinda like that. They will get it in time. Playing the game with minimal knowledge with people that they don't know can be stressful. It can also be disheartening to be called a noob. Ask my fiance.
Step 2, Don't go off and do your own thing: Not at first at least. When you first started playing the game, how lost were you? Did you know where to go next? Did you know where quest mobs were etc? If you are off doing dailies while your significant other is struggling questing, then you are not doing your part. They got into the game for you. Give them the time they need to develope, and be there each step of the way. Show them new thing, and if they like them, they may try to do them on their own eventually.
Step 3, Follow the into the Rabbit hole: Helping them reach their in game goals (no matter how boring or ridiculous) is a great way to get them to keep learning and playing. My fiance love achivements and has an odd fascination with Mechanostriders. We ground out the Gnomer rep that she needed for her "ridiculous", as she calls it. She loves that mount. I bought her some pets and she was instantly hooked. I showed her how to look up pets on the AH, which she does every time she logs on now. She is up to 47. She recently decided that she wants the Black Battlestrider despite the fact that she can already get all of the other Mechanostriders for far less effort. Keep helping them with their efforts, and you will be rewarded for yours. /loving a bunch of critters may seem pointless to you, but to someone new, it can be interesting and fun.
Step 4, Make agreements and stick to them: Most of the time, you are going to want to do two different things. Obviously, compromise is the best answer in this situation. For example, you want to quest and they want to PvP. Agree to do an hour of PvP if they do an hours of questing. You may hate PvP, but they will love you for helping and it will help your in game bonding.
Step 5, When the time is right, take a step back: Much like a mother hen, eventually you have to let them loose. They will find some kind of independence and run off doing their own thing. Let them do it. This makes them feel much more self sufficient and important in the game world. This could be anything, from going into a BG on their own or just running around the world picking flowers or exploring. These activities help bring up their in game self esteem and confidence. They don't need you every moment. They are able to stand on their own two feet. It can be liberating.
Just like real life, this is a relationship. If you treat mistreat them they will lose interest. Treat their in game avatar as special as you treat their RL avatar and you will be in for a double dose of fun.