There are two reasons children have tantrums: either the child is experiencing an intense emotion or she is trying to bully you into submission.

Part 1. Emotion-induced tantrums

This kind of tantrum is not about a power struggle, but rather it is about teaching your child how to manage stress or deal with emotional pain. Emotions like frustration, loss or even excitement can be overwhelming and scary for someone new to the world. The key is emotional regulation. Toddlers are not capable of this and therefore you need to model it for them.

What to do

Remain calm. Gently hug your child (if she likes hugs) or soothe her using kind, repetitive words. Research says that the parent’s calm body encourages the child’s body to release oxytocin and opioids, thus bringing her back into emotional balance. She will start to feel calm and safe as she realises that you can help her to cope with her big feelings. Remember: never hold a hyper-aroused child while angry. Your stress can increase their feelings of stress.

Name the emotion for the child. Famed psychoanalyst, John Bowlby, stated that children need to be allowed to freely express themselves through tears when expressing feelings of loss (e.g. when an enjoyable game is finished) or separation. Rather name the emotion by saying, “Sad. Johnny is feeling sad”. Bowlby felt that telling a child not to cry can lead to repression of painful emotions, which can have negative consequences in later life. Do not tell her to stop crying.

Respond empathically. This helps her feel safe and she learns to regulate her emotions in a healthier way later on. If you use punishment like putting her in her room alone, or ignoring her tears, she will stop crying, but not because she has calmed down. An ignored child becomes quiet because she learns that her parents will not be responding. Her brain and body, however, are still flooded with stress hormones that she is not old enough to know how to deal with.

Try to prevent the tantrum by:

Using distraction (e.g. singing, pointing out interesting or funny images)
Giving her a simple choice (e.g. between two shirts)
Before taking something away or ending an activity, allow the ending to be processed by counting to 10. It will go a little like this:
  Mommy, “It’s time for bed. Say bye-bye to Teddy.”
  Allow her to hold Teddy but gently put your hand on it as well. If she snatches it away, don’t become angry.
  Mommy, "Mommy will count to 10 and then we will say goodbye to Teddy. 1,2,3, say bye-bye to Teddy, 4, 5, 6, 7, 8, say bye-bye to Teddy, 9, 10. Ok now say, 'Bye-bye Teddy'." 
  Remove Teddy gently. The first few times you try this, it may result in tears, but eventually the technique will help her to process that a loss is about to occur and it will give her time to process the transition. - Lauren Bloch.