Allah is not understandable to any of His creatures, we can at most get closer and closer to Him and understand His influence on His created universe. Here (in Persian) and here you can find probably a good guide how and to what extent can we understand Allah. In what follows I try to give you a start point to start from.
The best symbol that describes Allah to His creatures is the pronouns He, Him, I (when used by Allah Himself) and etc. A secret without a key to resolve it. These pronouns can point to the very intrinsic nature (ذات) of Allah, but there exists no attribute to clarify it better for us:
وَلَمْ يَكُن لَّهُ كُفُوًا أَحَدٌ
And there is none like unto Him [112:4]
However, when we come to play and our knowledge of God is questioned "He" will be introduced as Allah, Al+Ilah, "the god" or God. Ilah comes from either Alaha اَلَهَ or valaha وَلَهَ and implies "god", a being that is worshiped or is so wonderful that we will at most be perplexed in. At this point we can say nothing about Allah what He is, but instead what cannot be Allah, like He is perfect and no imperfect being can be Allah. This "being perfect" is indeed the defoinition of being god, and can be used to prove one and only one god exists. This is where the four cornerstones of Islam is put forward (also the wisdom behind Ka'be having four corners according to Imam Sadiq --peace be upon him):
الحمد لله، سبحان الله، لا الٰه الّا الله، و الله اکبر
Praise be to Allah, Glory to Allah, there is no god but Allah, Allah
is the greatest
After these we should remain silent unless Allah Himself tells us something about Himself, we cannot on our own side say if Allah is forgiver or revenger, we can say these only after Allah Himself tells us he is the Forgiver and The Revenger. See how the holy prophet --peace be upon him-- stated this in the Hadeeth of Qadeer:
… وَ لا یَجِدُ أحَدٌ کَیفَ هُوَ مِن سِرٍّ وَ عَلانیةٍ، إلّا بِما دَلَّ
عَزَّ وَ جَلَّ عَلی نَفسِه
… And no one would find out how He is from mentioning the secrets or
the obvious symptoms, unless with His own guidances toward Himself.
And Allah has guided us toward Himself by stating what is now known as the Husna Names of Allah, each describing one aspect of Himself, non being fully understandable to us but each only defining a chain of concepts that we can improve in their perceiving but never reach its ending limit which is Allah as He influences our universe.