Well, the things I did to get my toddler to sleep was first of all to build up a pre-bed routine, and being -very- consistent with it. For us it's always; pyama's on, brush teeth, read bedtime stories in my bed, then put him in his own bed, alone of course, a bedtime kiss, all lights out and I'm out of there. You'll have your own rituals ofcourse, but I found that consistency really helps him/her understand that it's bedtime.
Personally, I think laying down with her while falling asleep might not be the best of ideas, I'm afraid you might end up 'teaching' your kid not to fall asleep alone, which is exactly the opposite of what you're trying to achieve if I understand you correctly.
I had the same problem with my son at that age, and I only managed to get him to fall asleep (alone) just by sheer consistency. At first it caused a lot of sleepless nights, but eventually it started to work (might take a week or even a few), and by now he's even eager to go to bed and sleeps very fast (like in under a minute).
I also found it really helps to explain clearly why you want your child to fall asleep alone, and why it's important for her to sleep properly, I'm still amazed at how much children of that age are able to comprehend and understand.
So in short my adivise is, have a bedtime ritual and be very consistent with it (also make sure your partner is on the same page), and if you want her to sleep alone, then stick with that and don't go sleep together. Well, that's what worked for my kid, but with all kids being different I can't give any guarantees ofcourse