Costume Parts are an integral part of Dead or Alive 6 as you will need to collect them in order to unlock additional outfits for the characters. Once you have the required number of parts which is usually between 500 - 1000 you will be able to fully unlock and equip the outfit by going to DOA Central and spending the specified amount of Player Points. Player Points is the in-game currency and can also be used to purchase accessories and titles for the character. Once an outfit has been fully unlocked it can be equipped from DOA Central or before online matches.
Costume Parts can be earned in Quest mode by completing all the missions in a quest. Each time you complete a mission you will be rewarded with a set amount of parts for a specific outfit for a particular fighter. It is also possible acquire parts by playing ranked online matches and Arcade mode but the yeild is low. There are certain outfits that can only be unlocked by doing DLC or Story Missions.
You can check out the different characters' outfits by going to DOA Central and Wardrobe and clicking on the characters whose different styles you want to view. This is done by pressing A or X on any slot and scrolling through the 'Costumes' section. You will see the amount of parts you will neeeded to purchase an outfit displayed by the number next to the blueprint icon to the right of each style variation's number in the list. To equip unlocked outfits you select it in the pre-match selection screen or in DOA Central to make it your default.
Check out our How to Earn Player Points Fast to learn how you can get this currency quickly to spend on character outfits.