To participate in Competitions, you have to simply play the game as you normally would and your efforts/stats will count towards the respective Competition: how much XP you make, how much Coins you earn, and how many Orders you complete.
When you enter Competitions, you are automatically assigned to your corresponding level bracket.
To participate in the XP and Coins Competitions, you have to reach level 5. For the Orders Competition, you need to reach level 21.
Also, if you want to participate in Competitions, make sure that this option in your Settings is NOT CHECKED, like in the image below.