Once you have reached the quest "Put On New Clothes" (Chapter 3 in Year 1), you will be able to change your outfit and appearance at will by tapping on the hanger icon at the bottom-left corner of your screen. There you can adjust your facial features and choose an outfit from your available options. You can unlock more customization options by leveling up and progressing through the game!
 
Please note, that the hanger icon might not be available in some scenes and locations. In such cases, simply open your character profile by tapping on your profile image in the top-left corner and the hanger icon will appear at the bottom of the following screen. If you still don't see it or are unable to open you profile, move to a difference scene and check again.