place an/the/(one's) order
To register an order for some product or service that one will receive in the near future. We placed an order nearly an hour ago, but we still haven't gotten anything to eat. I placed the order online, and they said it should arrive in two-three weeks. Please place your order at the window on the left, then go to the window on the right to pay for it.
place an order
to submit an order. My secretary placed an order for a new computer. I placed my order only yesterday.