Certainly it can't be as simple as knowing who he is. Even an evil spirit, before being cast out by Christ exclaimed, "I know thee who thou art." Yet evil spirits will not attain eternal life. So I must come to know Him on a more personal level. But how close? As close as a good friend, maybe a best friend?
I think the best example to look at Christ Himself. He said over and over that He did nothing of Himself. He only did those things which Heavenly Father would have Him do. He knew God so well that He knew how God would have Him act in every decision.
Aristotle referred to the conundrum of the man who is the best in a given field or vocation. To truly appreciate (deeply understand) how good this man is, a person must possess the knowledge that this man has. Otherwise, a person can offer praise but won't understand exactly what he or she is praising, because it is a mystery to those without understanding. Thus, the "best" man is the only one who can truly appreciate and fully understand what He has.
Well, that's just philosophy, but it may correlate with Jesus' example. He commanded us to "be... perfect, even as I, or your Father in Heaven is perfect." Perhaps Jesus Christ could fully appreciate and understand Heavenly Father's perfection, only because He had fully attained that perfection.
How well do I have to know Heavenly Father? I think the answer is "perfectly." Better get to work.