Usage patterns
〈人〉の順番が来るfor someone's turn to come
順番を待つto wait for one's turn
I'm waiting for my turn at the hospital.
順番を守るto keep to the order (not cut in line)
Everyone is lining up in order without cutting in.
〈人〉に順番が回ってくるfor one's turn to come around
My turn finally came around.
順番に〈動詞〉to do something one by one, in order
The students gave their presentations one by one, in order.
順番を決めるto decide the order (of turns)
Let's decide the order with rock-paper-scissors.
Expressions
順番付けるsequence; put in order; assign a sequence number