You can spend Miles under the 'Spend Miles' section of your rewards panel. Here you will find the number of Miles that are required to claim/get a reward/discount. Please make sure that you are logged into the rewards panel before redeeming your Miles. You'll need your Miles & More user name and password in order to spend your Miles.
Once you have enough available Miles, you can select 'Get' - again within the rewards panel; After confirming spending your Miles, you'll see the coupon code in the 'Your rewards' section. Apply the code during the checkout to get your discount. It's worth noting that only one reward is allowed per order.