After selecting Valentine from the character list, your first fight is against Peacock. Use the combo LPx3 > HKx3 (Low Punch 3 times, then High Kick 3 times) To do an easy combo that does a lot of damage.
The second girl your fight will be Parasoul. Again, use the same combo introduced when against Peacock to ensure victory.
After the small bit of story, you will go up against Painwheel. You can either use the combo I used when fighting both Peacock and Parasoul, or you can use QCF + HK (Quarter-circle foward + High Kick) to dash through your opponent, doing a lot of damage.
Your fourth fight will be against Cerebella, To win, you can either use QCF + HK or just spam buttons.
Your fifth fight will be against Ms. Fortune. Spam QCF + HK to do tons of damage, it should defeat Ms. Fortune.
The sixth person you fight will be Filia. Button mash for victory here.
Your final fight will be against Double, Valentine's assistant (usually). Again, use any of the methods I talked about earlier to win the fight.
After defeating all of those girls, you will face Marie, the final boss of any character's story mode. Click "Next Page" for some strategies on fighting her.