What has worked for me in the past is to figure out the cause of the tantrum first, and then act accordingly.
If you think it's because she wants attention, then igore the tantrum, and praise her and talk to her when she's being good. Sometimes it helps to place the child in a safe corner or spot to work it out (kind-of a time-out, but a little different).
If it is because she's frustrated, then igoring it isn't going to work. Try to talk it out with her. Say "Wow that is really hard to do, but you are doing a great job trying! Can I help you?".
If it is because she wants something she can't have, then calmly explain why she can't have it first. Then ignore the rest of the tantrum, and place her in the safe spot, if needed.
I only punished my daughter at that age when she did something wrong, not for the tantrum itself. They are just starting to talk and to try to work out their frustrations, and they can't help that. When I knew she was having a tantrum to manipulate me (she was 3), then I punished her for it. The tantrums went away quickly at that time.
I had some really terrible twos with my first daughter. My pediatrician gave me some good advice. He said I had to really try to set aside some time alone with her where I was COMPLETELY focused on what she was doing (it is harder than it sounds, since I usually multi-task without knowing it!). I noticed that she did get a lot better, but it did take time.
Good luck! Remember that you are doing a great job, and that you just need to be calm, firm, and loving. This phase will pass before you know it!!