I do have to disagree with this idea that you "must" teach children to sleep or they will never learn by themselves - of course they will, eventually. The only problem is it can take years, so I don't blame you for wanting to help her along a bit. My method isn't as quick as the controlled crying type method, but it might be more for you if you don't want to listen to her cry.
I don't know her level of understanding or how much language she has to tell you what is going on, but can you try to find out what is waking her? It could be something physical, thirst, hunger, cold, being aware that she needs a wee - or something in her mind, nightmares, waking up a bit and being scared because it is darker than when she fell asleep, wanting to know that you are close. (Don't ask her directly if she is scared at night, because if she is not, it's not a good idea to introduce the idea IYSWIM - just have a little chat with her about dreaming and night time and how dreams are nice and she might tell you what she does dream about)
If you find out what it is she is waking for, and it's something physical, then that is easily fixed/pre-empted like an extra blanket she can pull up if she is cold or a beaker of water by her bed. If it is something more psychological like a fear of the dark, or of being alone, or of monsters or bad dreams, then you can work with her to develop coping strategies so that she can go back to sleep by herself. Explain that you are just down the hall and that you are not going anywhere. Perhaps get her a nice nightlight - let her help choose. Nominate a teddy to be on "monster guard", or make up a "monster spray", or get DH to scare all the monsters away so that they never come back. Let her pick a favourite teddy or doll to cuddle if she feels lonely, or you might be able to do something like put "spare kisses" (invisible!) under her pillow when you put her to bed so if she wakes in the night and feels lonely she can reach for one and feel comforted. Or try introducing a sleep cue like a particular piece of music (a musical lullaby toy meant for babies' cots with a single push-button operation is best) as she falls asleep when you are there at the start of the night, that she can put on herself if she wakes in the night.
You can also explain to her what is expected of her at night. Toddlers like structure and schedules, and knowing what happens next. Make it into a fun activity - make a book together or a poster, with clear symbolic images or cut out photos of her doing each stage. Include all the steps in her normal bedtime routine, and then after that put a step or a page saying something like "If DD wakes up in the night, she can have a drink of water, cuddle her teddy and turn on her music box, then snuggle down in bed, close her eyes and wait for morning" and finally a page or a box showing the morning, being bright and sunny and her waking up or you waking her up, whatever normally happens. Then put the poster up in her bedroom where she can see it or read the book with her every night/day.
You may find at first that she still wakes in the night but you can then point to the poster or just remind her of the page in the book "DD, when you wake at night you can turn on your music box and snuggle up in bed." You or DH can sit at the end of her bed, but after a few nights tell her "I am still here. I am going to sit on this chair where you can see me. You snuggle down in bed." and sit where she can see you, but as far away from the bed as possible, until she is asleep. When she is happy with this, tell her "I am going to sit by the door, just out of sight. I am still here. You snuggle down in bed now." You may have to make reassuring noises at first so that she knows you are there (and also, don't let her sit up to see that you are there, keep telling her to lie down) then when she is used to that, sit just outside the door, go back in if she cries and reassure her, shhh, time to sleep now, I am just outside the door, I am not going anywhere. Once she is used to this and doesn't cry for you to come back in, then you should be able to close the door and leave her, and after a while of this, you may even be able to just go up to her door and say "Time to go to sleep DD. Put your music box on." or whatever sleep cue you have decided to use. Eventually, she should be able to get herself back to sleep, with props or not, and then hopefully she should start sleeping through.
Good luck!