Found with Tom (and again with Amber) that choosing your battles is important for your sanity and for the sake of the little devils listening. Set too many nos and they just won't listen because you become background noise. I find best way to tell if it's worth fighting about is whether or not it'll hurt anyone. Example if child decides to push the same toy of a table over and over again it's not worth it. There's no diff between a broken toy and a toy that's taken off them except they learn more quickly from one than the other. If the kid decides to throw said toy at someone then of course this needs correcting.
Be persistent. If you choose a way to deal with things then stick by it. Never ever never give in because the next thing you try will take longer to have an impact. This is because they realise if they push hard enough they can get what they want. Give a method of dealing with things about 2 whole weeks of trying. That gives it a good run especially as toddlers can be persistent little things.
When it comes to tantrums themselves. Ignore it. If you need to step away for a breather then do so just remember that toddlers throw fits because they don't get that they can't have everything they want and lets face it, none of us really like being told no. By not interacting with them when they're kicking, screaming, holding breath, the tantrums won't last as long even if the first few times feel like forever.