As this question was asked in a religious category, I will try to provide some of the answers useful for judging religious stories. However, the same principles often apply to non-religious stories.
Science
If a story so contradicts accepted science that even a miracle could not explain it, then the story is fiction. An example is the first creation story in Genesis, which says that God created the light of day on day1, but did not create the sun, moon and stars until day 4. He even created plants and grass before the sun, when the temperature must have been close to absolute zero.
Parallels
If a story in the Bible closely parallels older stories from the same region, it is probably derived from those older stories and therefore really factual. For example, the story of Noah's Flood closely parallels the story of the flood in the Epic of Gilgamesh.
Doublets and multiple versions
If there are two or more different versions of the same story in the Bible, then one or both of them must be fiction. Just a few examples:
- Noah's Flood
There are actually two slightly different stories of Noah's Flood in the Bible, so cleverly woven together as to appear just one, slightly complicated story. When Genesis was being redacted, the followers of each story were not willing to give up their special story, so both were included. One clear example of the doublets is in Genesis 6:19-20, where Noah is told to take two of every animal onto the Ark, and in Genesis 7:1, where he is told to take two of every unclean animal, but seven of every clean animal. Similarly, one story has the flood subsiding in just forty days, while the other says that it lasted one year.
The two different authors of the biblical stories of Noah are called the Priestly source and the Yahwist. The verses attributed to the Priestly author are: Genesis 6:9-22, 7:6, 7:8-9, 7:11, 7:13-16a, 7:18-21, 7:24, 8:1-2a, 8:3b-5, 8:7, 8:13a, 8:14-19, 9:1-17. The verses attributed to the Yahwist are: Genesis 6:5-8, 7:1-5, 7:7, 7:10, 7:12, 7:16b-17, 7:22-23, 8:2b-3a, 8:6, 8:8-12, 8:13b, 8:20-22. - Abraham
Genesis gives two parallel stories of Abraham where he got tangled up in his deviousness. First he told the Pharaoh that his wife Sarah was his sister, for fear that the Pharaoh would kill him in order to have sex with her (Genesis 12:13), only to be found out and banished from Egypt. Later (Genesis 20:2ff), this time for fear that Abimelech, king of Gerar, would kill him in order to have sex with his by now quite elderly wife (Sarah was now over 90 years old and stricken with age), Abraham again said that Sarah really was his sister. - Isaac
The story of Isaac so closely parallels that of Abraham that it even has a parallel story in which he tried to pass his wife Rebekah off as his sister to the same king, once again for fear that the king would kill him in order to have sex with her (Genesis 26:6-11). It is likely that the entire story of Isaac was copied from that of Abraham - The two nativity stories of Jesus.
The two nativity stories, in Matthew and Luke, are so mutually incompatible that at least one, and probably both, must be a literary creation by the authors of the gospels. The position of most liberal scholars is that the stories of the birth of Jesus are simply not based on fact, and that there was no virgin birth, no angels and no wise men or shepherds who came to worship Jesus. - Genealogies of Jesus
There are two genealogies of Joseph, father of Jesus, both demonstrating that he was descended from King David. In Matthew, Joseph's father is Jacob, while in Luke, Joseph's father is Heli.
Structure
If the story structure is so artificial that it can only have been fiction, then it was fiction. A few examples are:
- Genealogies of Jesus
There are two genealogies of Joseph, father of Jesus, both demonstrate by use of numerology that Jesus was destined for greatness.
Matthew demonstrated that there were 14 generations: from Abraham to David; from David to Josiah; from Josiah to Jesus. To do this, the author had to ignore 3 kings in the Old Testament and have David in the preceding (as 14) and following (as 1) groups, but not so Josiah.
Luke had great men occur in multiples of 7 generations starting from Adam, with: Enoch at 7; Abraham at 21; David at 35; Jesus at 77. It also had: Joseph at 42 and 70; Jesus (Jose) at 49. To do this, the author had to insert his own fictitious people into the Old Testament list: Kainan at 13; Admin at 28. - The first gospel
Mark's Gospel is divided into two divisions that mirror each other quite uncannily.
The first division begins with John explaining the coming of Jesus, followed by the baptism and the voice of God from heaven, and ends with Jesus predicting the passion story. The second division begins with the Transfiguration of Jesus and the voice of God from heaven, and ends with his passion story, followed by the young man explaining the departure of Jesus. The coincidences are so improbable, including the improbable sequence, that the possibility exists that some important events in the story of Jesus are fiction. - Good Friday
Mark organised the account of the death of Jesus in a twenty-four hour cycle, neatly divided into eight three-hour segments, beginning with the Passover meal at 6:00 o'clock on the evening before his arrest. After the traditional three-hour meal, he went to pray on the Garden of Gethsemene, but three times (once each hour) had to berate the disciples for falling asleep. He was arrested at midnight, then taken before the Sanhedrin at 3:00 oclock in the morning - the start of the watch known as the cockcrow. Then, three times (once each hour), Peter denied Jesus. At 6:00 o'clock, when it was morning, Jesus was taken to Pontius Pilate, and was placed on the cross at the third hour - 9:00 o'clock in the morning. When "the sixth hour had come" (12 noon), darkness covered the whole earth for 3 hours, then Jesus died. He was buried before 6:00 and the start of the Jewish Sabbath.
Historical accuracy
If the story contains significant historical inaccuracies, then it is probably fiction. Some examples are:
- The story of Abraham tells about Abraham walking to the land of the Philistines, nearly a thousand years before the Philistines arrived in the Levant.
- The story of the Exodus tells of cities that had not yet been built, if it took place in 1440 BCE.
- The Book of Daniel confuses Kings Darius and Xerxes, along with many other historical errors.
- The Book of Esther also contains many historical errors.
- Luke's Gospel says that Jesus was born during the reign of King Herod, who died in 4 BCE, but also during the census of Quirinius, which took place ten years after his death, in 6 CE.
In other instances, you may find sufficient reasons to believe that a particular story actually is true. Undoubtedly some stories in the Bible are true, or at least contain truth. And in some cases you will decide to suspend judgement, because a story is sufficiently credible that it might have been true, but there is no extra-biblical evidence to support it.