Hi L.,
I have a 3 and a half year old daughter, and went through this same thing with her about a year ago. Here's some suggestions:
1. make sure you have a bedtime routine. You have to start the routine about 30 min before you want her in bed. Our routine is usually bathtime, blowdrying hair, brushing teeth, letting her have water, potty then off to bed. Some people read books but I don't do that with my daughter at bedtime.
2. She is testing you by calling out to you and asking for things to stall the process. You just have to be firm without losing your temper (easier said than done, I know) but you have to try really hard! =) Just firmly tell her no to whatever she asks for. Unless it's something like a drink of water or potty I usually tell my daughter no. If she cries, I just let her cry and act like I am not bothered by it. I leave the room then come back and she calms down, but I don't give in to what she wanted. I explain to her firmly that it is time to go to sleep.
3. One thing a friend of mine does that works for her child, is she gives her daughter two tickets. (handmade with construction paper). She told her daughter she can use a ticket for something but if she uses both of them then she has to give up her dollie. It works for her. I've never had to try it but you could maybe manipulate it a little to work for you.
The main thing is to try to stay calm and patient. Try starting the bedtime process a little earlier so you won't feel such a rush to get her to get to sleep and won't feel as stressful on you. You have to be consistent. She's definitely testing her bounds, so you have to let her know what is not okay. I like to compare it to speeding. If we knew that every time we sped we would get pulled over and written a ticket, we would not take a "chance" on it. But we know there is a chance there won't be a cop around every time. It's the same thing with the kids. If you let them get away with it one time, they will remember it forever and keep trying to get away with more and more.
Best wishes! I have a strong willed daugher also. My best advice is to stay calm.