Oh no it's definitely normal around the age of 1 :)
Tantrums aren't naughtiness at this age, though, it's just when they get really overwhelmed by their emotions. It's the first time their brains are really developing enough to experience them (I'm sure babies must have emotions but I think they are far more simple and probably more baseline: fear/pain and happiness)
Basically, you wouldn't expect them to have control over their emotions at the age of 1 (or at 2, or really very much at 3 either) and IMO ignoring them doesn't actually help them learn how to control their emotions or react in an acceptable way, so it's not really helpful.
What is important of course is to not let the tantrum change how you would have reacted, so if you've already said no, not to backtrack and change your mind. But equally if the situation is (for example) you've said they can have one biscuit and they're kicking off because they want two, I wouldn't take away the first biscuit.
It can help to try and "reduce the WTFness of being a toddler" (to steal a wise MNer's words!) by warning them in advance what is happening next, in a way that they understand. Never say "in five minutes" but use events, e.g. "We will play one more game and then it's time for bed" or "After going on this swing it's time to go home". When she gets a bit older you can give her more control by saying she has time for 3 more things at the park but she can choose. Oh, you can also use this for safety stuff like "When we get to the big road you have to go into the pushchair".
Also try and be aware of concepts/instructions she doesn't understand, like "Share" "calm down" etc - to use the sharing example, at their age the concept of playing with something that somebody else is using at the same time is utterly incomprehensible. Plus when adults barge into their argument saying "Share nicely" it doesn't help, because they don't innately know what the word sharing means - you have to teach them and show them. I find that the concept of turn taking is FAR easier to explain/model for this age group and more of an age appropriate expectation too. Start off with an item/toy which the actual playing part is short but only one person can physically play with at a time, like a ball or a slide. You sort of hold one child back at the top while letting the first go down, saying "Tommy's turn" then when Tommy has finished you let Jessica go, saying "Jessica's turn" and repeat, prompting them to line up and wait, get out of the way at the bottom etc. With a ball you use this as they kick/roll it to each other. They get the idea. Once they understand turns, then it's easier if another child is playing with something they want, you just say "It's Tommy's turn now. Your turn later."
I think verbalising the emotion and also allowing her to experience things like frustration, sadness etc in a safe environment help - don't always rush to fix everything for her or help if she's struggling (e.g. to build a tower) - use words to encourage and say "Never mind, try again!" and when she is sad about something, just hold her. It's really good and healthy for her to learn that there's nothing wrong with feeling sad/angry/frustrated, but that it's not okay to express these by hitting or screaming or whatever.