S.H.
My son is 4... he has been napping, everyday... since he was a baby.
If not, he turns into a Troll.
He does not last all day, pleasantly, without a nap.
PER his age currently, he naps in the afternoons. Anywhere from 1:00-3:00. He naps 2-3 hours, and STILL goes to bed at night, just fine at a normal hour of 8:30pm.
For naps, since has has done this daily, since a baby, it is just auto-pilot. No battle about it. It just is 'routine' everyday. He knows it.
ALWAYS verbally 'cue' your child, it is nap time "after lunch." Give your child a head's-up about what is coming up. PRIOR to nap time, have a WIND-down time.... (it being ab out 1/2 hour for my son), making EVERYTHING calm/quiet/turned off/boring/darken the room(s). This is part of our 'routine' before nap, with my son.
You NEED to 'cue' the child. They will not just do it on their own and march right into the room, by themselves. They are 3 years old... you assist them and cue them.
I always tell my son "After you play, then nap time... we get ready...." and he knows that. I give him 10-15 minutes to play and go full circle with it, then we put away and get into the nap routine. No battles. Because I CUE him. You need to do that with young children or any child.
All the best,
Susan