Ana is a powerful support hero. To master her abilities, you need to practice a lot.
If you are familiar with Nova's Snipe, it won't be hard to adapt.
Positioning is key of success. Try to avoid confrontation and stay behind as possible.
With your huge range, it won't be hard to heal your teammates.
Consider saving your Biotic Grenade to save yourself in dangerous situations.
Although, the heal negation could be very useful in teamfights.
If you miss with the Sleep Dart when you're in trouble (1v? situations), you are basically dead.
Ana is not mobile at all. The great range comes with a price.
If I want to describe her very shortly, I would say, she is a combination of Nova (skillshots, requires good positioning) and Sgt. Hammer (big range, huge impact, low mobility).
We'll see how she fits into the meta, but her package is very decent.
Have fun!