Basics
Tired or hungry children are susceptible to tantrums, so offering a snack to a hungry toddler or putting a cranky child down for a nap is a good idea.
Distract
You can sometimes tell when a tantrum is brewing. If so, distract your little one by doing something a bit wacky - point to the elephant hiding behind the door, phone someone using a banana or start talking in a funny voice. Kids don't have long attention spans, and will find this silly thing so amusing they'll forget all about why they are upset.
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Whisper
Some of us easily fall into the trap of trying to out-yell our child - this will usually exacerbate the situation. Instead, try whispering. Your toddler will try to figure out what you're saying, and settle down. (Note, this technique only works a few times before you little one smartens up and ignores your attempts at whispering.)
Ignore
This is easier to do at home than in the middle of the supermarket. Provided your little one is not at risk of doing anything harmful, just ignore their outburst and carry on doing what you were doing. A tirade is often an attention-seeking act, so ignoring the actor may stop them in their tracks.
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Repeat
I've never had much success with this tactic, but the idea is to keep repeating why your little one can't have whatever it is they're after, or do whatever it is you don't want them to do. Say the same phrase eg, "come and sit down for dinner" over and over in the same neutral tone no matter what your child does to resist. The idea is they will eventually get bored and just do what they're told.
Play
Have a few games up your sleeve, such as I Spy, This Little Piggy, Peek-a-boo, or Round and Round the Garden. That way, when your little one's temper starts to rise, you can engage them in an activity.
Cuddle
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When a tantrum has passed over into the full-blown fit phase, no amount of games or silliness will help. Cuddling your child can soothe you both and bring the situation under control.