So of course all children are different, but here are some things that work really well for my LO:
1) A consistent nap and bedtime - I try really, really hard to be mindful of her being home in time for her nap (1 pm) and bedtime (8pm) so that she is used to always sleeping in her crib.
2) A wind-down routine - this is crucial for my daughter. She has a hard time transitioning from play-time to sleep-times without it. I put her in her sleep sack, read 2-3 books, lights out, and then I nurse her and sing her some lullabies. She then goes into the crib awake, but drowsy. She has her special blanket and a stuffed toy in there that she likes.
There are occasional days here and there when she just forgoes the nap entirely, but even on those days, she'll relax in her crib and have quiet time. For bedtime, she usually chatters in the crib for awhile before falling asleep.
We've been doing this same routine since around 6-7 months, which was the time when I had reached my wits end with her crappy sleeping habits. The routine has helped tremendously and nap/bedtime is no longer a big stressful event for us anymore.
As far as the separation anxiety goes - when you try to "hand her off" - are you doing so confidently, or do you tense up? I just ask this because kids are so smart and can read your emotions, so if you have reservations about handing her off (because of past experiences where she's been upset over it), then she might read into your tension and continually get upset when you do so.