Believing there is a God is not the same as trusting Him as your God and Father... Many people believe he exists but that doesn't make them his children...
James 2:19-20 KJV
 Thou believest that there is one God; thou doest well: the devils also believe, and tremble.
Only by a relationship where we place our trust in him and his love for us and we know him as Father can we be his children. You must be born again... Born of the Spirit. Just like you must be born into an earthly family you have to be born into God's family by the spirit of faith
John 3:3-12 KJV
 Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God.  Nicodemus saith unto him, How can a man be born when he is old? can he enter the second time into his mother's womb, and be born?  Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God.  That which is born of the flesh is flesh; and that which is born of the Spirit is spirit.  Marvel not that I said unto thee, Ye must be born again.  The wind bloweth where it listeth, and thou hearest the sound thereof, but canst not tell whence it cometh, and whither it goeth: so is every one that is born of the Spirit.  Nicodemus answered and said unto him, How can these things be?  Jesus answered and said unto him, Art thou a master of Israel, and knowest not these things?  Verily, verily, I say unto thee, We speak that we do know, and testify that we have seen; and ye receive not our witness.  If I have told you earthly things, and ye believe not, how shall ye believe, if I tell you of heavenly things?
I can say that I believe in airplanes and that I believe an airplane can take me from here to there, but if I’m afraid to get on it, I reveal that I have no ‘faith’ in that plane. Also, if I do not get on the plane, I have no reason to expect it to take me anywhere. I must exercise my ‘faith’ in that plane, by boarding it, if I am to receive the benefits it offers. Likewise with Christ, I can say I believe in Christ but if I am not trusting him with my life do I really have faith in him? See the difference?
Faith results in changed actions
True faith is evidenced by a change in the way we act. We no longer want to do the things we used to, such as only living to please ourselves, God changes our "want to" and gives us new desires that come from him and are pleasing to him.
Romans 8:5-6 KJV
 For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit.  For to be carnally minded is death; but to be spiritually minded is life and peace.
True faith comes from him (Holy Spirit) and through his word (Jesus Christ) and calls Him Father (Father God)
Romans 10:17 KJV
 So then faith cometh by hearing, and hearing by the word of God.
True faith results in a changed worldview, we begin to see things from an eternal perspective the way God sees them. It is important to see more like God if we want to understand Him.
Look at John 3:12 again...
John 3:12 If I have told you earthly things, and ye believe not, how shall ye believe, if I tell you of heavenly things?
Faith results in changed priorities
Suddenly God becomes more important to us than anything else and we develop a hunger and a thirst for him and his word.
Matthew 5:6 KJV
 Blessed are they which do hunger and thirst after righteousness: for they shall be filled.
Believing can be a passive mental acceptance of a fact but have no transforming effect on our life. This is mere belief apart from trust and is not equal to faith. This comes from the mind and the lips but not from the heart and doesn't affect the heart.
Believing can also be a deep heartfelt conviction of truth which always causes a change in the believer's thoughts, actions and priorities. This comes first from the word of God then gets into the hearts of people and causes a change of mind in them.
This is true saving faith.
1 Peter 1:23 KJV
 Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever.
Hebrews 11:1 KJV
 Now faith is the substance of things hoped for, the evidence of things not seen.