The process is quite easy. When you accumulate enough miles on your Discover it Miles card, you should use it to buy a ticket (any airline ticket). Then log in to your Discover online account (if you don’t have one, register it) and when you see this transaction, you can apply your miles to it. To do it, click “Redeem Miles” in your online account, then click “Travel Credit” and choose the Travel Purchase which you want to pay for with miles, and you are done.
Another way to redeem Discover miles, is get cash as a direct deposit to your bank account and then use cash to purchase a ticket. Discover also allows to redeem by phone (look for the number on the back of your card).
Whichever way you redeem, the value is the same: 1 mile = 1 penny. Discover miles cannot be transferred to any loyalty program, however, you can redeem without any blackout dates or other limitations.