Sleep problems?

I don't know if this is a normal phase my daughter is going through but lately she has become a real terror when it comes to bedtime. She was really easy to manage in the beginning sleeping for around 12 hours a night and asleep by no later than 9. But nowadays she always wakes up again at midnight or just before, even when she's had dinner and a bottle and in bed by 8 or 9. It always takes a few hours to get her back to sleep usually needing another nappy change and bottle before she can settle. I've heard its good to get them used to falling asleep on their own within the 1st year but we seem to have got stuck in a routine of me always having to lie beside her and give her cuddles just to get her to sleep. I have tried putting her straight in her cot and leaving her to settle herself instead of lying with her but she always ends up screaming and making herself frantic which ends up with my partner getting no sleep either. I just wanted to know if any other mums have the same problems and what are some solutions to get her to sleep by herself and at a reasonable hour? I realy want to find a solution before the next baby arrives!