By default on the Trading Page your Open Orders, Order History, and Trade History are available at the bottom of the page beneath the chart. This Orders Pane may be hidden or viewed by clicking on the Clock icon on the Layout Panel on the left of the screen.
The Open Orders tab includes all the necessary information for each order a user currently has open including a unique order ID, the date and time the order was placed, trading pair, order type, price, and amount. At the right of each row is the option to cancel the order.
The slider marked Hide Other Pairs will hide any orders currently open for trading pairs other than the one currently displayed on the Trading Page. Clicking the icon directly to the right of that will expand the Orders Pane to fill the screen, and the X will close it.