The Holy Quran describes the story in Chapter 2, Surah Baqarah, from verse 246 to 251. We believe the Qur'an is the word of God which is unchanged and unfabricated and 100% true. However the bible has gone through much distortion and fabrication. Therefore the story of Talut in the Quran is the accurate version.
There are historic references in hadith litrature but scholars are careful in taking these as they have to match the Quran.
Here is a lecture on Talut that I gave that you may benefit from: