It was said in the Torah, that one may divorce his wife handing her a letter of Divorce, But what was the practice among the Arabs before and after Prophet Muhammad?
The only things i could find about pre-islamic talaq is:
That talaq was not limitted so you could speak out talaq as often as you like and could get back your wife as often as you liked. As it seems during the 'Idah. Many spouses used this to hinder the wife to marry somebody else. So they spoke out the words of divorce then right before the end of the waiting periode declared reconciliation before giving divorce again and so on.
Islam made an end to that saying that you may -only- divorce twice with the option of reconciliation (2:229), but if you divorced again this women is free to marry somebody else.
There were also types of talaq which are technically not talaq but a prohibition for the sexual desires and needs of the woman or wife:
dhihar الظهار which means declaring the wife as similar as one of his mahrams, so he would never ever touch her again.
Eyla' الإيلاء which means the husband makes an oath to never ever touch his wife again this would mean that the wife would have to wait at least 1 or 2 years until her husband might again share her bed.