DD started losing it at 10 months, but after about a truly horrible week I tried very hard to see the world from her point of view and blimey, it was an unjust and frustrating place.
She's now almost 2, and has regular paddies but they really are just beyond her control. Frustration and intense, whole-body disappointment when things don't go right (and it's not just getting her own way - same thing happens if she's tired and she can't get teddy's jumper on her head, for example). Luckily they're relatively short-lived and after a couple of minutes getting it out of her system she'll either allow herself to be cuddled or distracted.
The only way I can deal with it without yelling 'get a grip, I can't change the laws of physics' (which I do occasionally, cos obviously I'm human) or doing her physical harm, is to empathise energetically (oh babe, it IS very frustrating isn't it), stick to my guns (if I'm the cause of the melt-down) and leave her to calm down. I check on her every 30 seconds or so to make sure she's safe and tell her I'll be in the kitchen/wherever when she wants a cuddle.
Of course, I have only the one child to deal with and she rarely does it when we're out. She does flip out in shopping trolleys quite often, but I find a bit of running up and down the isles (I have no inhibitions, me), spinning round and 'oh look, grapes! let's eat some now) fends most of them off at the outset.
Oh, and BIG ditto giving warning about things that are about to happen, particularly having to leave a game, get out of the bath etc. We count down 5, 3, 1 minute til... Doesn't stop the protests entirely but made one hell of a difference when we first tried it.
Good luck!
Oh, and I have a theory about these early paddies (I'm sure I'll be eating my words in a year, but hey) - I reckon if I can be absolutely firm about never backing down in the face of a meltdown now (ie when they're out of DDs control), she's less likely to use tantrums later, when she could throw them deliberately, cos it won't be worth it, she'll know it won't change my mind about anything. So maybe the early tantrum throwers will turn into nicer 3 year olds? I desperately hold onto that optimistic thought when we're having a rubbish day!