My daughter won't sleep!

My 18 month old daughter has never been one for sleeping a whole lot. Now that she is getting older it is getting harder and harder to get her to sleep. She has always slept in our bed and usually falls asleep in my or my husband's arms. She has regrettably never learned to fall asleep on her own. So if we can't lay down with her for whatever reason she is a bear. Also sometimes she just won't fall asleep. I don't know why. She can be super tired, but instead of sleeping she just goes and goes. As long as she gets whatever she wants she is fine, but if you tell her no she throws a fit because she is so tired. I don't know what to do. I have tried letting her cry in her crib, but I can't do it. We got up to 20 minutes of her just screaming then I quit. I couldn't handle it. Also during that time period she was extra clingy to me and extra whinny. I am at my whits end. I want her to get the sleep she needs, but I also want it at predictable intervals. So life can move on without tiptoeing around naps. I would like to create a schedule and have nap time at nap time. I don't know how to do this. We have always just let our daughter tell us when she is hungry or tired and worked around that. For infants this strategy is fine, but as kids age and become more vocal and active this no longer works.