K.D.
This is such a tough age! There's so much out there about "terrible twos", but so little about what to do when they hit a year early! From your daughter's point of view, she knows exactly what she wants and she expects you (or her other caregivers) to know it. But she doesn't have much verbal skill at this age, so when her intentions are misread, or when she wants something she can't have, she throws a tantrum. Every time. Loudly. Endlessly...
What can you do? First, help her out with language skills! Sign language can work wonders, but also spend some time just repeating her sounds back to her. The repetition will help - really. Try to anticipate her desires - does she always want to touch a certain lampshade, is she fascinated by the cat's tail, is she constantly trying to get over a certain gate? Some things can be rearranged to be less frustrating for her, and some can't. That's life. Try to remove some of the frustrations, but also accept that tantrums are going to be part of life for the next few years.
Sometimes, your daughter will need to know you're there for her, even if you don't know how to help, or can't for whatever reason. She's still a baby - it's okay to "baby" her when she needs it. But it sounds like she's also going to be a bit stubborn. So when she's just frustrated because she can't have something, you'll need to ignore her. It's a fine line, and you won't always handle it right.
I always tried to imagine each situation from my daughter's perspective - was she tired/hungry/overstimulated to begin with? Is her frustration justified (did another kid take the toy she was playing with)? Or is she just expressing her dissatisfaction with life in the loudest manner possible? For the first two, I would comfort, for the last, I would ignore until she calmed down a bit.
As for violent behavior, you definitely did the right thing! Throwing things at any age is not okay. Put her in a safe place, and leave - that is, stop interacting with her.
As she gets more verbal, the tantrums will change (and hopefully lessen!), but you'll actually be much better at coping than a lot of the other moms of 2yo's you know - you'll have had practice, and you'll have already established the words you use and the consequences for certain behaviors. I know, it doesn't make it easier now, but it will get better.
Around 18 months, she will be mature enough to start using time-outs - one minute for each year of age is the standard I have used. Used consistently, time-outs are great discipline.
I feel your frustration! Remember, it won't last forever! You're doing a great job.
-K.