I’ve a 3 year old. We go through a bedtime routine after which the light goes off and I leave. She sometimes start wincing and whining on which i don’t respond. Most of the time she then settles herself within a minute. I only go in her bedroom again when I hear she’s really upset (you know the different types of cry), but will not pick her up out of bed. I taught her to fall asleep from when she was a little baby and compare my other children she has been the easiest one.
I have to admit that by my eldest daughter it went different. She was great in delaying and my husband would respond on her all the time, which only made it worse. We found that’s very important to be on one line as parents.

We had a list that I would go through. It included all the delaying bits ie; clean teeth, drink, kisses, stories, toilet etc. We would go through the list before bed reassuring both them and I that there was no reason that they should be up.
Another thing we did with my daughters was to read a meditative book. We used The Wishing Star by Marneta Viegas. The stories take your child on a relaxing journey and calm them. I would turn off the light and use a book light to read by. Remember to change or omit the end phrases – often they would encourage the child to come out of the meditation and go on about their day. I use to modify by adlibbing my own words. The book can be found on Amazon, ad they give you a couple of sample stories there to try. Good luck working through this stage. ♥ https://www.amazon.com/Relax-Kids-Wishing-Marneta-Viegas/dp/1782798706

My daughter is about the same age and has done the same kind of stalling tactics. We’ve found keeping her room down from the beginning, no harsh overhead light helps keep things calm from the start. We have a routine of saying goodnight and I love you’d, and turning off a little nightlight. Then hubby leaves and I lie with her and sing her to sleep. ‘Over the rainbow’ is currently a favourite, as is ‘Morning Town Ride.’ She sometimes asks to get out of bed, but as I’m lying on the outer side she can’t get out, and after a little while she just drops off.

From memory of watching The Nanny, her tips were routine. Once they’re in bed, you ignore delaying tactics. If they keep getting up, you pick them up and put them straight back in bed, no conversation.

I have heard fantastic things about the Gro-Clock! Its a clock with a screen that pictures either a sun or moon. When the moon is up, its the time kids stay in bed and when the sun is up, they can come out and start the day!