Act One
Part 1: Carver / Bethany
Note 1: You can only get one costume change, not both.
How to get costume change: This is unavoidable, but you have a choice. You can bring your sibling with you down to the Deep Roads with Anders, and make them into Grey Wardens, who will return to fight with you during Act III's end, or you can let them stay at home. If at home, Carver will join the Templars, and if Bethany is at home, she is induced into Kirkwall's Circle of Magi.
Details:
Grey Warden: Mainly silver armor, with the Griffin Emblem on the chest, with streaks of blue and white chain mail, covering the stomach.
Templar: You see the armor all over the damn game. See the Gallows if you really want details on Carver's armor.
Mage: Bethany gets an aqua/blue mage robe, with gold embroidery on the shoulders, and on the waist, with white coloring her sleeves, and by her waist/hips.
Part 2: Aveline
How to get costume change: Pass the first year, and she becomes a guard, changing her outfit once. Secondly, to get it upgraded again, complete her quest "The Way It Should Be". She is now appointed Guard Captain, and gets newer armor upon entering Act Two.
Details: Mainly silver armor, with hints of orange cloth by the shoulders and an emblem of the guard on the chest. The shoulders get more layers of orange in Act Two, and her legs have black chainmail with silver pointy knee caps.
Tip: Raising Isabela, Fenris, and Merrill's Friendship/Rivalry to 50% is recommended by Act II.
Act Two
This guide presumes you do no other quests besides Blackpowder Courtesy after Act II starts.
Part 1: Fenris
Note 1: If you're going to romance Fenris, you may want to change Isabela's costume first.
How to get costume change: You must get to about 50% Friendship or Rivalry. It doesn't matter which. During Act II, take Fenris outside of Kirkwall, and you'll start the Bitter Pill Quest. Hire the Elf, and tell Fenris you did it so she could have a job. Second, let Fenris deal with Hadriana however he feels like. Use the star option, and then flirt. Head back to your mansion and flirt again.
Head to Fenris's mansion and begin initiating conversations with him, and flirt every chance you get. You can even choose to give him his gift [Found in a sack, by the allienage at night; The Book of Shartan], and flirt there as well, and finish his Questioning Beliefs. Return home, and initiate romance.
Now decide if you wish to; continue the romance or break it off. Regardless you get, his costume change, and I believe no disapproval or approval. [Need Confirmation]
Details: Fenris gets a red ribbon/scarf tied to his right arm, and bears a tiny Amell/Hawke emblem on the left of his belt.
Part 2: Isabela
Note 1: If you're going to romance Isabela, you may want to change Fenris's costume first.
Note 2: Isabela's outfit is tricky. If her costume change is done after Fenris's there's a good chance it'll appear. Otherwise, you may need to go to the Black Emporium and get a bottle of Maker's Sigh and use it on Isabela to get the costume.
How to get costume change: Have about 50 % friendship or rivalry [Friendship is preferred due to the fact Isabela has a chance of leaving this act], and simply flirt to her when you can. Finish her Questioning Beliefs, and head home to the Estate. You may want to give her gift to flirt one extra time [Ship in a Bottle, right before you exit the Smuggler's Cut in Blackpowder Courtesy and meet the dwarf.] Head home and initiate romance.
Choose whether to keep going with Isabela with feelings, or to stop. Either way her costume changes. Mostly likely no approval or disapproval [Need Confirmation]
Details: She gets a black corset, added goldwork embrodiery to the bottem hem of her sash, a piece of red cloth around her right bicep [Hawke's Favor?], and replaces the leather pauldron on her left shoulder with a metal one.
Part 3: Merrill
Note 1: If you choose to upgrade her armor, you lock off all other romances. So if you want to romance Anders, there's no way to upgrade Merrill's armor, and if you want to upgrade Fenris/Isabela, you need to do it before Merrill.
How to get costume change: Simply get Merrill to 50 % Friendship or Rivalry, and take her Mirror Image Quest. [For easy Rivalry, deny her the reward and she gets uber pissed, but still willing to romance] She gets her Questioning Beliefs quest after Mirror Image. Flirt with her during every oppurtunity you can as well. Finally after Questining Beliefs head to your Estate. Initiate romance. [Her gift is a wooden halla, and bought from the Dalish, but provides no flirt option.]
You can choose to break off the romance, but you won't be able pursue another.
Details: Merrill's new armor is a set of white/silver chainmail with plate shoulders and elbow pads and leathers robes with a light blue sash around her waist.
Act Three
Tip: Only one more armor change left in the game.
Part 1: Anders
How to get costume change: Complete his personal quest; Justice
Details: Ander's Robe becomes mainly all black.