I know exactly what you are going through - it can be so frustrating sometimes! Unfortunately, though, what I have to say probably won't make you feel any better...
First of all, the "Terrible Twos" typically start much earlier than 2. Much of the literature I've seen says 18 months, but in my experience (from talking to lots of moms) it seems that they start at about a year, give or take a couple of months (which would be where your daughter is...) My daughter started throwing little tantrums around 10 months; the big ones started at 11 months. Basically tantrums happen because toddlers have all these REALLY big feelings that they A) don't understand and B) don't know how to deal with them. Add in the inability to communicate (much). I know if I was dealing with all that at once, I'd probably scream and cry too.
I know the tantrums are untwanted behavior, but try to look at them from your daughter's point of view. For example, she's sitting in your lap, and sees something shiny on your face, she thinks "wow those look like fun!", so she grabs them to have a little fun. Then, instead, she gets a frown, a no, and the "toy" is taken away from her. Just imagine how frustrating that would be. It's good that you try to explain to her "they're expensive" or whatever, but it will be some time before she understands...
Which brings me to my next point (sorry, this is getting long-winded). While there are varying opinions, most people will tell you that a 10 month old is too young to "discipline," and I agree for the most part. However, she can LEARN. The key is consistancy. If EVERY SINGLE TIME she goes near the fireplace, for example, you grab her RIGHT AWAY and redirect, at some point (after many many MANY attempts) she'll learn that every time she goes there, she gets moved, and decide it's not worth the trouble. If, however, on her 10th try, you DON'T grab her, she'll think to her self "sometimes I can go over here, sometimes I can't" and keep trying, hoping for another chance. As parents, we REALLY have our work cut out for us!
I highly recommend "Happyiest Toddler on the Block" - if nothing else, it will teach you a lot about what's going on in your daughter's head.
Also, I know it's hard (I have a 16 month old and a 2 month old...) but when she's doing something "against the rules" try to remember it's her JOB to explore the world and find out how things work (when I let go of a toy, it drops, when I throw a toy, mommy yells, etc)
Good luck, and as always, this too shall pass, and you'll probably look back and miss it (well, some of it...)