How does Islam say that God and man may know each other? Or rather, what is the relationship between God and man in Islam?
The method for becoming Muslim is to say a two fold formula ‘no God’ (negation) ‘but God’ (affirmation). This is a summary of Islam’s World view; that every thing is not God, but everything is a sign of God and so in someways is God. The religion is about firstly removing the veils from one heart of what is not God and working on being able to behold God in everything.
In Islam God is seen as both Transcendent (distant) and Immanent (near), without taking away anything from either. To give a really full account would be quite complex, but hopefully this summary may help.
God’s Essence, that which He is in Himself, is unknowable. Most theology in Islam has focused on this and generally concerns itself with what God is not. We would not say He is Love because we would say that presumes too much, we say He is Loving.
God’s Immanence is via everything; the entire universe is seen as an Act of God, So we are experiencing God directly at every second of every minute of every day. God is One and from His perspective there is just God, but from our perspective we experience Him and it is infinite. It is these different experiences that we define and call His Attributes, such as Mercy or Wrath. Islamic mysticism - Tasawwuf - focuses on this, and concerns with what God is.
God exists and is All Being (His essence) and so is the only one that truly exists, we exist but only contingently through God. The universe is not God in its outward form, but its inward meaning is command and so is God, so in that way we could say the table is not God, but inwardly its meaning points towards God; a single disclosure of God. The whole universe is a complete revelation because it manifests all of God’s attributes.
God can also be known through the revelation of the Qur’an, which is His Divine Speech.
Mankind is the single most complete example of God’s attributes - we are made in his image. So we can see a unique disclosure of the Divine in ourselves and others. Muhammad (peace be upon him) is seen as the perfection of mankind and the greatest single self disclosure of God where he exhibits all the Attributes of God in perfect harmony.
So Islam offers an Absolute God that is in no way manlike, but a direct relationship without any intermediaries through every single thing in existence.
Much could be said, but I hope this at least gives a broad outline