Upon entering the main game you will find on the middle right-hand side of the screen the Quests button, you simply tap on it to access the Quests Menu.
Upon entering the Mission menu you will find provided the Mission refresh timer indicating how much time is left until it is refreshed (C). You will also find the missions you have successfully completed (A) which grant you various Rewards which you collect by tapping on the Collect button. The missions you have yet to complete are listed (B) with their accompanying button indicating you have not completed them yet. Each respective mission has a description of what needs to be carried out in order to complete it successfully written above their respective progression bars.
Within the menu, you will also find that you can find out what are your Daily Missions (A), Weekly Missions (B) & Lifetime Missions (C). In addition, you may also see what Rewards you are to earn by tapping on the little yellow information button (i) on the top the right of each Chest located on the top progression bar (see image below).