If you place a limit order on the order book it will stay until it fills or expires.
Note that cancellations are transactions sent to the blockchain. If your cancellation is sent with a low gas price it may take longer to cancel. It is still possible for another user to fill your order if their transaction is mined before your cancellation.
If you would like to cancel an open go to the account tab.
In the OPEN ORDERS tab select the orders you wish to cancel by checking the boxes on the far right and pressing the "Cancel Selected" button.
If no orders are currently selected there will be a button to "Cancel All Orders". This will submit a cancel transaction for all open orders across all order books.
Clicking the cancel button will prompt you to sign the transaction in your wallet.
Alternately you can click on the little green wallet next to your order on the order book.
This will bring up your order in the order handler and the option to cancel.
This will bring up the gas handler if you are using Ledger or the Metamask confirmation.
Be aware that cancelling an open order will cost gas because it is sending the cancellation to the blockchain.
To see information about what costs gas see the article When Do I Pay Gas?