According to Catholicism, how should one read the Catholic Bible? Is there any order that we should follow to read the bible?
Like whether we should follow some chronological order or just read randomly.
I am just starting to read the Catholic Bible and don't know where and how to start.
There is no general rule for how to read the entire Catholic Bible. I have done it from beginning to end, by reading the Sacred Scriptures for a little over a half hour each morning until I finished with the book of Revelation.

Personally, I chose at least a half an hour of reading each day because the Church permits one to gain a plenary indulgence if one reads Scriptures devotedly for a half an hour a day.


  Some ways of obtaining a plenary indulgence include:
  
  
  Praying the rosary in a church or oratory, in a family gathering, within a religious community or canonical association of the Christian faithful, or in any context in which the faithful come together for this purpose;
  Spending at least half an hour in adoration of the Blessed Sacrament;
  Praying the stations of the cross at a location where they are legitimately erected (e.g. a parish or shrine);
  Participating in a preaching mission at a parish (e.g. during Advent or Lent);
  Reading the Bible for at least thirty minutes.
  Visiting a special site of pilgrimage. In the Archdiocese of Toronto, the Shrine to the Martyrs in Midland has been a site where pilgrims can obtain a plenary indulgence since 1644.​ - What is an indulgence?
  


Reading the Bible from beginning to end can be quite a challenge to some of the faithful. What I found helpful is to incorporate the biblical readings of major feasts into the equation...

For example, one could read the Passion of Our Lord Jesus Christ from the Gospel of St. John on Good Friday. 

At Christmas one could read the those passages concerned with the Birth of Our Lord.

Many more examples could be mentioned as follows: 


Transfiguration of Jesus (August 6) - (Matthew 17:1–8, Mark 9:2–8, Luke 9:28–36) 
The Assumption of Mary into Heaven (August 15) - the reading of the Mass of the Assumption 


As I have already mentioned, there are no general guidelines on how to read the Bible. It is hard to read it from cover to cover without a little deviation in the course of its entirety, so break it up if necessary in order to persevere. 

One could also read 15 minutes from the Old Testament and 15 minutes from the New Testament if desired. The choice is yours.

Another way would be to read 10 minutes from the Old Testament, 10 minutes from the Psalms and then 10 minutes from the New Testament.