T.K.
Hi M.!
As sad as it is to hear it, it's very normal behavior. Still-emerging language skills, a fierce desire to become independent, and undeveloped impulse control make children this age prime candidates for getting physical. Of course that doesn't mean ignoring it. Let your toddler know that aggressive behavior is unacceptable and show her other ways to express her feelings.
I always gave my son logical consequences. For example, if he gets in the sand box and starts throwing sand, I immediately take him out and sit with him while we watch the other kids play and explain he can play again when he's ready to play nicely like the other kids. I never try to reason with him, like saying "How would you like it if someone threw sand at you?". Toddlers don't possess the cognitive ability to imagine themselves in someone elses shoes. They do understand consequences. Just be consistent and diligent.
I always have to remember to keep my cool, which is very hard sometimes! Yelling or telling my son he's being bad never works. When I reacted calmly and controlled my temper, he got his under control better. Afterall, we are setting the example as parents.
I make sure I always, always, always to respond immediately when my son is aggressive. He should know instantly when he's done something wrong. I always remove him from the situation for a brief time-out (but only for just a minute, after that he won't remeber what he did and won't make the connection that his behavior put him there). I found this was the best way to let him cool down. After awhile he connected his behavior (for example, hair pulling) with the consequence (the time-out) and figured out that if he pulls hair, he ends up out of the action.
I always make sure I respond to each episode the way I did the last time. That way, he will came to expect my response, and set up a pattern. Eventually, in sank in that if he misbehaved, he got a time-out. I responded the same way even in public. There were times I was mortifies, but I didn't let my embarrassment causeme to lash out at him. If people stared I just brushed it off with a comment like, "The wonderful stafe of terrible twos", and disciplined him in the usual fashion.
Sixteen months is a little young to be teaching alternatives, but I started my son in the habit of it. Afterwords, I always talk to him. Because he can't communicate to me what set him off, I usually try to communicate to him, like "Yes, Christopher, I know you wanted to play with the telephone, but it's not a toy. It's not Christopher's phone. Maybe you could have played with Christopher's phone (hand him his play phone). It's not nice to hit. It ouchies Mommy. You need to use your words." He can't say sorry yet, so I always make him give a hug to the person he hurts. That way it will become a habit to eventually say sorry when he's hurt someone.
I always reward my son's good behavior, even sometimes over exaggerated praise. Sometimes it doesn't even have to be about behavior. Everytime my son usues the words he knows to express himself, I always say "Good words Christopers. Great job!" And I give him a hug. That way he can realize how powerful words are.
I always let my son have physical outlets. He gets stir crazy. So I always make sure we get outside to play. We go to parks, take lots of walks, and explore the neighborhood. He's a much happier kid when he's played otuside 2-3 times a day.
This is what has worked for me thus far. Just remember it's a stage! You'll get through it! Good luck!!