Thoroughly acknowledged the difficulties of their situation, acknowledged that they are very busy, etc. In other words, you need to actually listen to them and proactively appreciate them before you play the role of advice-giver.
A friend told me this today and it rang true.
Suppose you tell a busy person: "You should check out this museum — they have a great Asian Art exhibit." A busy person’s first quiet thought might be, "I’m a busy person, I can’t just go to museums whenever I want." He will discount your advice because you haven’t acknowledged a basic fact about his life.
Now suppose you preface your suggestion: "I know you’re really busy. But you should check out this museum — they have a great Asian Art exhibit." I would expect a higher follow-through rate.
Most people think they are busy. Many people annoyingly make a big deal out of how busy they are. Whether it’s self-delusion or reality, it’s important to acknowledge the busy-ness of those we work with — both verbally ("I know your time is valuable…") and in our actions. Chronic tardiness to meetings with other busy people is a sign of arrogance as it implies one does not respect the other people’s time.
The giving and receiving of advice has long fascinated me. Here’s my post on overvaluing advice when the problem is hard and undervaluing advice when the problem is easy. Here are more general thoughts of mine on the topic. Here’s my post on how disclosure of one’s bias doesn’t cancel out its effects — ie we don’t account for the bias of an advice-giver as much as we should, even when we know it’s there.