If you can stay on top of the calendar, phone sheet, and contacts, you’ll probably be able to relay a lot of information off the top of your head, which is great. But if there's too much to remember, have a system for finding the answers to simple questions very quickly (for example, you could bring your phone or laptop into a meeting so you have easy access to the calendar). But that's only half the battle. You've also got to have a solid strategy for finding information that isn't as readily available.
Sometimes you'll be asked for information that requires a little digging. This is when you’ve got to be resourceful. When asked a question you don’t know the answer to, respond with “let me check,” or “I will find out," and then check, find out, and report back promptly. Make it seem effortless. Never admit that you don't know the answer, or worse, that you don't know how to find the answer. Do whatever you can to figure out the information on your own, without asking others. If you simply don’t have knowledge of a company process and there's no written material you can comb through to learn it, ask another friendly assistant for help. Try to avoid asking others on your team, especially if it's outside of their purview. If you’re constantly pushing work onto your superiors, it will get back to your boss, and you won’t be able to maintain your image as a person who can magically produce information out of thin air (aka a rockstar assistant).
Strive to be the person that can come up with the correct information the most efficiently — it will set you apart from others and show your boss that you're indispensable. If your boss thinks you know everything, he’ll begin to trust you with higher level tasks relatively quickly, which is how you’ll eventually earn that promotion.