New story Missions are unlocked when you reach a certain Star level.
Daily Missions are updated every day. There are 6 daily Missions, and 3 are displayed at a time. Select a card to see additional Missions. Note that you can complete only 3 Missions, so you can choose which Missions you want to complete that day. 
Weekly Missions are updated once a week. You'll receive 3 stacks of Missions. A new Mission is revealed once the previous one in the stack has been completed. The Missions become harder as you go through a stack, but the rewards get bigger!