How do you get a 3 year old to take a nap?
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too old to "take a nap". Some kids don't.
What time do they go to bed?
What time do they get up?
What time do they eat breakfast/lunch?
What time is this nap you want them to take?
What are they doing between breakfast and lunch? Lunch and nap? Is it physically demanding? Are they watching tv?
What is there "to do" in room?
What is their objection? They're old enough to say WHY they don't want to nap.
Sometimes they're too busy. Too engaged in the world. Too much going on.
There are a lot of factors to "diagnose/suggest" over the internet without knowing a lot more about your child, your lifestyle, your habits, your home, your environment, your parenting style , and - most importantly - the personality of your child.
Maybe suggest a "quiet time" - they don't have to "take a nap", but they DO have to sit quietly in their room by their self and "read" or listen to quiet music. Sometimes they drift off then. Sometimes they don't.
We had a "special nook" in my son's room - we called it his "play space" - some cute fluffy stuffy pillows - his were sports shaped, but any will do. A colorful thick comforter on the floor - a shelf of books (that also acted as the divider) - and it was a cozy child sized little spot. A little music player he could operate. He loved it. Didn't nap that often, but was quiet in there. And many mornings I would go in to find him sleeping in there instead of his bed. 
just some things to think about.
Response to Alisha-Bunny-12 (Original post)