You need to take the toys, books and you laying with her out of the equation, no caving in. Toys in the bed send a mixed signal. Get it clear bedtime is just that, time to sleep.
My kids are good sleepers and I contribute that to just laying down the rule bedtime is bedtime. No negotiations, it is just time to go to sleep. It is my downtime and it isn't always perfect or smooth but it is the same time every night, same routine and my kids know what to expect.
Set up a structured bedtime routine, good bedtime for a three year old is around 7pm, depending on her napping.
Then go through your routine, brush teeth, hair, wash face, jammies go into bed, read some books, kisses and hugs and walk out the door.
If she gets up, don't say a word and put her back in her bed. Continue it. Also if she does this a few nights remind her that if it is going to be a battle her bedtime will be earlier then following night. That works like a charm for my kids!:)
If she thrives of visuals, put up a chart, for every night she goes to bed, stays up and goes to sleep, a star, for every 14 stars a special treat or surprise. For every night she pitches a fit, take one away. Then after a while the chart isn't even necessary as she just knows what is expected and does it. Praise her for her doing it too, big time. Then it becomes a habit she is falling asleep on her own. Don't be stern or yell as that elevates blood pressure in everyone, be matter of fact "it is time for bed, let's go get ready" and do it. If she cries, you can warn her once "well you have to go to sleep, if you pitch a fit no story and I don't want that for you"...if she continues make sure you follow through. When my kids were really young we did the three story rule, if they started to whine or cry around bedtime they lost a story, then another if they continued until no stories. If they did great, then all three stories could be read and they were to go to sleep.
But firm tough as she has conditioned herself to having to have you fall asleep with her or be entertained. Make it clear what the rules are and don't sway. It won't be overnight but in a few weeks she will get the message and go to sleep herself. It takes you being firm and not giving in. Let her scream, pitch a fit, whatever but be very clear what you expect out of her and consequences if she does not follow those rules.
I am not being harsh, nor is it mean, but doing this for her is a positive as she will sleep better and when parents lay with their kids until they fall asleep, it is setting them up for dependency, so when she wakes up and you aren't there she needs you to go back to sleep. Giving her the gift of a good nights sleep will benefit everyone!
Good luck!