Mina: She responds well to a professional approach with an occasional suave response (Basically, when she flirts with you). Doing things by the book and arresting people also sits well with her. She dislikes a gung-ho approach. Good ways to increase her early are doing well enough in the Weapons training for her to give the 'bonus mission' and complete it, and complement her to Westridge during the interrogation. You won't romance her till just before the final mission, and she's with you a long time, so she's the easiest to romance.
Madison: Like Mina, responds well to professional with an occasional suave. Taking her as your Handler for Marberg's mansion is advised (This will cause a small drop with Mina). Keep her spirits up by telling her how useful she is, and thanking her for helping. Once she moves into the Rome safehouse, don't leave the city. You only need a +3 or higher relationship to be able to romance her. You'll know it's time when she says she is tired and going to bed. One more mission, and then you can wake her.
Scarlet: Reasonably easy. Be suave with her on the plane, switching to professional when she starts flirting back. In the Taipei mission where you infiltrate the hotel, respond to Scarlet in a professional manner, she gets angry if you try to use her as a honey trap. If you bug the CIA safehouse in Rome, you'll be receiving confidential emails from halbech about naughty things they're doing. Forward these to Scarlet and be professional. Finally, you won't get to romance her until just before the final mission. When you do go to see her, be honest with her, and you get the option to romance. If you're not honest with her, you get the cold shoulder.
SIE: Probably the hardest to romance, as it requires you to take a specific path through the game. First, don't go to Moscow until you complete Rome, and in Rome's final mission, choose to disarm the bombs instead of saving Madison. SIE hates Marburg, and foiling his bomb plot pleases her when you first meet in Moscow. Be aggressive with her initially, switching to suave when she flirts back. Make a deal with her and agree to co-operate. When she emails, flirt back. When you first go after Surkov, in the American Embassy, choose SIE as your handler. This results in you gaining VCI assistance during the storming of Brayko's mansion. During that mission, choose to save SIE (pretty obvious really if you want to romance her). After this, she disappears, so Moscow is the only window you have to work on gaining relationship with her. When you reach the final mission, choose SIE as your handler. The scene where you can 'romance' her is very obvious. Just be flirty with her when she's talking to you, and 'go with it'.
credit to feystruck. _gamespot forums.