1. Because we are finite and God is infinite (unlimited), we can fully never know God. It's true we can know God, but we cannot know him (or his attributes/characteristics) completely. Psalm 145:3 affirms that his greatness is "unsearchable."
2. There are two kinds of attributes to God*: (i) Incommunicable Attributes and (ii) Communicable Attributes
Let me explain with an example:
A communicable attribute is God's wisdom, because he can communicate this to us (i.e. we can also be wise).
An incommunicable attribute is God's eternity (i.e. we can never be eternal like God).
3. When you read the Bible, look out for the Names of God. In Scripture, a person's name is a description of his/her character. For example, in the Bible, God is compared to a lion (Isa. 31:4), an eagle (Deut. 32:11), a lamb (Isa. 53:7), a fire (Heb. 12:29), the bright morning star (Rev. 22:16), etc. Taking from human experience, the writers of Scripture also describe God as a judge (Isa. 33:22), doctor (Ex. 15:26) and a father (Deut. 32:6).
4. Here are some helpful resources:
c. Who is God? An article by Matthew Slick.
d. Get your hands on this groundbreaking book by one of the world's top scholars, J.I. Packer.
e. Get your hands on another great book about God by Chip Ingram.
f. Finally, read Mark Driscoll's On Who is God is a short, 1-hr. read, but includes a list of God's characteristics. See below!
[Answered by HM]
*See W. Grudem, Systematic Theology (Notthingham, England: InterVarsity Press, 1994), 156-225.