This is a great question. There are many ways in which the Bible can help a person to be at peace and stable in life. Let me give a few way that are time tested by those who have lived with the Bible.
First, when a person reads the Bible they come to realize that God is a God of love. He is also in control and therefore whatever befalls a person is at the hands of a loving God. This is not to say that life will be easy, but that life will be filled with his grace and love. Paul says in Romans 8:28:
"And we know that in all things God works for the good of those who love him, whohave been called according to his purpose."
Second, the Bible also says that God's peace comes upon believers when they pray and are filled with thanksgiving. Part of this happens, because there is an acknowledgement that a person is not alone. For this reason, Philippians 4:6-7 states:
"Do not be anxious about anything, but in every situation, by prayer and petition, with thanksgiving, present your requests to God.And the peace of God, which transcends all understanding, will guard your hearts and your minds in Christ Jesus."
Finally, the Bible reminds people that what they need the most they have - namely salvation. This alone causes a person to rejoice and be at peace. I will add a mediation on the Psalms, which speaks of peace.