In Street Fighter 5, each of the characters only have access to two costumes at launch (without pre-ordering). This includes their default outfit plus the alternative one they wear in the storyline. You can also unlock up to 10 different colors too.
Unlocking the second costume is simple because all you have to do is play and complete the Story Mode with each character. They should be wearing the outfit during the Story Mode, but by completing it you should be able to use it in other modes.
However, you won’t be able to use the Story Mode costumes in other modes yet until the Shop option opens up. Capcom is set to open the Shop option as a free update that will be given out to all players in March. Once the Store opens, the Story Mode costume should be available for you to unlock to play in other modes in Street Fighter 5.
At the start of the game, you only have access to two colors. You can unlock six more additional colors for each character by beating the Survival Mode. If you play through the Easy Mode in Survival, you unlock the third color option. In Easy Mode, you only have to survive through ten matches only.
If you play through the Normal Mode in Survival, you will be able to unlock a fourth, fifth and sixth color option for your character. Normal Mode is a bit harder because you have to survive through 30 matches. You need to complete all 30 matches in order to get the new colors.
Playing the Hard Mode in Survival you will unlock the seventh, eighth, ninth and tenth colors for your character. You have to beat 50 matches successfully. The Hell Mode does not unlock colors, but you get more Fight Money and a new title for beating 100 matches.
Bear in mind, you only get to unlock colors for the character that you are using. If you want to get all of the colors for each character, you effectively need to play through the Survival Mode in Easy, Normal and Hard 16 times as each different character.