One of the most beautiful things about having a firm belief in God is that fear and worry simply escape one's life. I think this is due to two main reasons:
Having belief in God and doing that which He likes, guarantees His nearness and continuous care. We might think sometimes we are ourselves the masters of our own lives. We might plan, think ahead and work hard yet actaully nothing which takes places escapes God's will. An observed fact by faithful servants of God is that God's care and planning for our lives can lead to good things we had not thought we would achieve (on our own). The key is to have full trust in God and ask Him for whatever we want faithfully.
God's care for the righteous surely secures the servant from fears and worries in regard to his or her life and the future. Since, God is in charge of everything. God simply, by way of His power and will, makes life good for the ones who believe in Him. He does things for them, because they love Him and He loves them.
Belief in God and love for Him take away fear and worry and replace them with courage and motivation. The believer knows that all he or she needs to do basically is to love God, make good deeds and avoid all those things which lead to God's anger. In addition, he or she is asked to work, take care of the children, educate themselves etc..
Beyond that, God is in charge of the rest. A man should do his part and leave the rest faithfully and trustfully to God. Relying on God and trusting upon Him is a pillar of faith and one of the most important pillars of a happy and a calm life. Instead of having worries, the believer makes his or her part and relies upon God. A companion of God shall not fear or worry, because he or she is protected and guided through life by the eyes of God.
To summarize let us read this verse from the Holy Quran:
أَلَا إِنَّ أَوْلِيَاءَ اللَّهِ لَا خَوْفٌ عَلَيْهِمْ وَلَا هُمْ يَحْزَنُونَ (62) الَّذِينَ آمَنُوا وَكَانُوا يَتَّقُونَ (63) لَهُمُ الْبُشْرَىٰ فِي الْحَيَاةِ الدُّنْيَا وَفِي الْآخِرَةِ ۚ لَا تَبْدِيلَ لِكَلِمَاتِ اللَّهِ ۚ ذَٰلِكَ هُوَ الْفَوْزُ الْعَظِيمُ (64)
(62) Unquestionably, [for] the allies of Allāh there will be no fear concerning them, nor will they grieve – (63) Those who believed and were fearing Allāh. (64) For them are good tidings in the worldly life and in the Hereafter. No change is there in the words [i.e., decrees] of Allāh. That is what is the great attainment.
[10. Yūnus, Jonah]