There’s some information, but few details.
The exact details of everything that happened leading up to Salazar Slytherin leaving Hogwarts aren’t all known, but in Harry’s fifth year, the Sorting Hat tells a bit more about it.
“And never did they dream that they
Might some day be divided,
For were there such friends anywhere
As Slytherin and ...
In addition to the excellent information in Bellatrix's answer, I want to add a few more details that we know: (all non-book quotes are from the Chamber of Secrets article on Pottermore)
Salazar Slytherin had a grandiose opinion about his importance to the school:
However, it is clear by the very decoration of the Chamber that by the time ...