I went through the same sleeping problem with all three of my children. A friend loaned me a book with my second child that was a tremendous help. I'm sorry that I don't remember the author (my kids are now 10, 12, & 15), but the title was something like "How to Solve your Child's Sleep Problems".
Think about if you were to wake in the middle of the night and discover that your pillow was missing. You'd feel around for it, check the floor, etc. and when you found it you'd get comfortable and go back to sleep. There's a good chance that you wouldn't even remember the incident in the morning. If, however, you woke up and were unable to find your pillow, you'd be wide awake with the light on looking for it. You'd probably be angry and would even get out of bed searching for who took your pillow. Most of us wouldn't just roll over and go back to sleep without it.
If babies learn to fall asleep while nursing (as all of mine did), that becomes their "pillow". But their comfort could also be rubbing their backs, their pacifier, the sound of the TV, etc. They fall asleep the same way, but when they awake and find that their comfort isn't there anymore, they aren't able to just fall back asleep. They also can't go look for it, so of course, they cry. That's why, when she wakes up crying and you nurse her again, she falls back to sleep within a few minutes. She got her "pillow" back.
The steps to correcting the problem, as best as I can remember them, are as follows:
1. Put your daughter to bed while she's still awake, not after she's fallen asleep at your breast. She has to learn to put herself to sleep instead of relying on you.
2. When she starts to fuss and cry, let her do so for only 5 minutes. Then go in and talk with her, comfort her, and reassure her that you are still there, but DO NOT pick her up. You should only be in her room for a half minute or so, and then walk out again.
3. This time you let her cry and fuss for 10 minutes before you go in, and then you follow the same procedure as you did the first time.
4. Now you let her cry for 15 minutes before you go in and reassure her that you're still there, and reassure yourself that she's okay.
5. After that, you go in every 15 minutes until she falls asleep.
The first night is the toughest. It's hard to hear them cry, but this really works. Mine (I went through this process twice) lasted around 2 hours the first night. But amazingly, only about a half hour the second night. By the 3rd night, they were out right after the first 5 minute span. And by the 4th night, I didn't have to do it any more. I was surprised, relieved, and so thankful at how well it worked.
Good luck to you. I'd love to hear how well it works for you.