Watching other people (esp my fiance) saying "no" ever so gently has me wondering how easy life could be if I were able to do the same. I'm practicing it, and I think I'm getting better at it. Telling the other person the root cause why you say "no" helps a lot to instill empathy for your situation. The root cause always stems from a need or necessity that you currently have, like need for rest/food/time to think/time to finish this or that task properly/... Even if you are lazy and simply don't want to help right now, remember that this laziness also fulfils one of your needs - probably you need to rest or think.
ADDED: Telling people that you just cannot help _right now_ also softens the blow. Also, if it's a customer then delaying might even be more beneficial than just declining - you might need the billable hours in the following week.