Who can remember a parent actually pulling the car over on the side of the road in that last threat before, "I'll turn this car around?!" If your dad/mom did this, you knew they meant business, didn't you? If you say you are going to do something, do it, even if it is inconvenient.
The first trick is to not make empty threats. If you really wouldn't pack up and leave the restaurant, don't say it. If you're usually a mushball in this regard, say to your kids, "You know how Daddy always says, "We're going to go home if you...but then he doesn't really do anything? From now on, I will be following through with this." Expect to be tested. Be prepared to follow through. It should only take one time for your kids to test this, as long as you follow through. Yes, they might test this when YOU are doing something fun, so choose your consequences/threats wisely. If you are at a party and don't want to have to leave early, be prepared to have a back-up consequence.
Never say yes under pressure. Don't say no and then change your mind. Take a deep breath and think about your answer when your child asks you for something. Tell them you need a little time to think about your answer. If they persist, say, "If you want an answer immediately, the answer is no. If you give me some time to think about it, the answer might be yes (or no). If you ask me one more time, the answer is no, because you are harassing me, and I don't like it. Would you like me to answer now, or would you like me to think carefully about my answer?"
Be prepared. If you change the way you parent (even if you tell them you're going to do so) they will remember the one time they were able to get you to cave. It's called intermittent reinforcement. An example of this is your dog remembering that one time someone fed him from the diningroom table; even if it's been months since anyone did so, he's still there begging, isn't he? When you change your parenting and say no, your kids will "up the ante" so-to-speak and will try and try and try their darnedest to break you. Don't break!!! If you do, it will be ten times harder to break their habit the next time. Be strong!!
And finally, if you are not going to be consistent, you will lose credibility with your children. If you yell, swear, hit but say that they are not to yell, swear, or hit, you have lost your ability to influence your child through relationship. They'll respect you out of fear, but they will follow your example when frustrated. Get some help if you need to break your own bad habits; that will be modeling for your kids, too :)
Thoughts? Concerns? Questions? Anecdotes? Do share!