It is always good to try and keep one step ahead of your boss. Here are some ways I have found to do that:
Read the mail
Read all correspondence and look for action items and due dates and diarize them or bring them to your boss’s attention. If you have access to your boss’s Inbox you should be checking e-mails as well.
Check their calendar
Familiarize yourself with what your boss has scheduled for the week and beyond. Is there anything you need to do to help them? Make travel arrangements? Arrange a conference call? Your boss’s calendar is always changing, but it is a good idea to look ahead and be familiar with what is coming up.
Bring things to their attention when they need it
Keep a good bring-forward system to bring items to your boss’s attention. Use your Tasks in Outlook to remind you or diarize it on your calendar, but have some way of having things ready for your boss, when needed.
Second guess them
When they tell you they want to meet with someone have some questions ready. Things they may not have thought of. If you are organizing a meeting, is it a lunch meeting or do they need a boardroom? If it is a lunch meeting do they want you to make a restaurant reservation or have lunch catered in? Have a list of questions and think ahead. If you are arranging travel, have your list ready. What airport do they want to fly to? How many nights? Any preference on hotel?
If your boss is giving a presentation, find out the details and requirements from the conference organizers. Find out what kind of audiovisual equipment they have. Do they want you to e-mail a PPT presentation or bring it on a memory stick? Have the answers for your boss.
You will make your boss feel more secure when he or she knows you are in control of the situation.