There are many articles directed at women about how to say "no" at work, but this article (featured on Oprah) is different. Several executives discuss the real effects saying "no" has on a woman's career- -especially if she is trying to move up. I like how they shine a spotlight on a subject around which people often tip-toe.
I think it's like small children - don't tell them 'no' if you can reasonably say 'yes, later.' Can we have ice cream? Yes, later. Can you write up this report? Yes, later. You can almost always settle down someone whiny or someone having a meltdown with 5-10 minutes of your undivided attention.
I do things with my boss that may help - say things like "When do you really, REALLY need this? I'm working on the software story, the product awards due Friday, and the proposal for CBS. Is this new assignment a higher priority than those? Which of these projects would you like me to focus on first and which should I procrastinate on? On your way out, would you mind telling Steve that the CBS plan will have to wait?"
I also lie about deadlines as a general rule. If something is due Monday, I tell the contact or coworker or boss that it's due the Wednesday before and I'll be locked up until then. It may not even be a lie - I'll just say I need to get it done by X time, they don't have to know it's an arbitrary need.
When it comes to business trips I rarely say no, because I secretly enjoy them. Staying late is usually no problem, but I don't like it to be sprung on me last-minute - in which case I might try a no, but it would not be a hard no. I always say yes to cleaning up other people's messes - that's a sure way to position yourself as an MVP.
Also when people are asking you to do them a favor, like stay late or push aside another project, they're in a weakened position, so you can extract something out of them - in which case it's good to say yes and get something back. Like "I was supposed to take my cat to the vet tonight, but I could switch that to tomorrow morning and come in around noon instead."
I've never been asked to relocate, but I'm 99% sure that would be a big fat NO.
Of course this stuff is much, much easier for me than for some of the women in the article, since I don't have to deal with soccer games or PTA meetings, and my career eclipsed DH's about ten years ago so my job needs take precedence!