The Clothing Closet
When you first start your farming adventure, you will select the facial style, hair and eye color, clothes, and hair style of your main character. After you work with Gunther to upgrade to the Decent House, you will be able to visit the character customization options. The Clothing Closet will be located in the back of the house. Once you upgrade to the Big Farm House, the closet will be relocated to the west-side of the house.
Walk up to the Closet and press the A Button to open its options. You'll be able to Change, Put Away, or Take out. Time will not move while you are making changes to your appearance, it won't cost you any money to use the Closet, and you can do this at any time of day.
Change
You can change your character's outward appearance from the Change menu. In the game you'll be able to make and select from 4 skin colors, 9 face styles, 38 hair styles, 17 hair colors, 17 eye colors, 158 clothing outfits, 42 hats, 23 glasses, and 42 accessories.
Each of the nine categories have options you can select from. Navigate through the options by pressing Up or Down on the Circle Pad or Directional Pad, then press the A Button to move into that category's options. The Skin Color, Face options, Hair Style, and Hair Color options are all available once you build the Decent House; you don't have to do anything in the game to unlock them.
There is one eye color that can be unlocked. The Heterochromia Eyes becomes a prize from the Fashion Show once you win at least 10 times. This option will give you one blue eye and one yellow eye. While there is a Lavender hair color, there isn't a Lavender eye color.
Note that there are facial styles for the girl main character and the boy main character, and you can only select the options based on your gender (i.e., you can't choose boy face styles if you're playing as a girl).
Hats will change your default hair style to the one associated with the hat. Any Accessory (Acc.) that you equip will not visually appear on your character, but they have other benefits such as earning color points during the Fashion Show or triggering stamina-related combinations. You can wear up to 3 accessories on your character, but you must select/deselect each one individually.
When selecting your options, you may press the Left Shoulder and Right Shoulder buttons to rotate your on-screen character.
Put Away and Take Out
The Put Away option is how you add items to your Clothing Closet. Clothing, hats, eyewear, and accessories are crafted by using your Sewing Studio, then must be placed within the Closet in order to wear them. You can have multiple copies of the same item in the closet, but you can only select it to wear one time; for example, you can place two Crimson Rings in your Closet, but when selecting a ring to wear you'll only be able to equip one of them.
If you do add something that you don't want in your Closet, use the Take Out option to remove it and place it back into your bag.