No is a tricky word, because you always want to be perceived as a can-do individual. In general, you should try to preempt situations in which you will have to decline an assignment.
A good first step is to formalize your daily responsibilities with your official boss. Find out who on your team is authorized to delegate work to you, and note the type of assignments you can expect from each person.
If someone who is outside your core group of delegators gives you an assignment, politely reply that you would be glad to help, but that you would appreciate it if she would check with your manager first. The person may or may not pursue the matter, but, either way, you have extricated yourself from an awkward situation and have placed the ball in your boss’s court.
On the other hand, what if someone who is a member of your core group of delegators gives you an assignment that you don’t have time to attend to? If you don’t speak up, you will only become more buried, so tell him that you wish you could assist but won’t be able to attend to the task until you’re finished with the urgent one that’s currently occupying your time. Are you uncertain which task is the priority? Ask your boss – that’s what she’s there for.
Now, here’s the toughest scenario. What if your boss is the one who is overloading your to-do list? I recommend saying something such as, “I’d be happy to take care of that, but today I’m researching statistics for next week’s client presentation. Which do you think I should do first?” Again, you have made someone else accountable for deciding which of the competing tasks you should direct your energy toward.
Note that in all of these cases, you have actually declined to take on a new task, but the word no and the phrase I don’t have time are absent from the conversation so you won’t sound prickly or be perceived as uncooperative.