Once you reach the main menu of the game just click on Lobby, where you would usually go for the matchmaking.
There you will find both your daily and weekly challenge and the requirements which you will need to furfill. After completing the individual task, you will receive an item (mostly a gun or consumable).
A few of these challenges might actually take some time.
You can see your progress on this particular challenge, e.g. killing 5/10 Hives.