Recently, I heard a preacher say that "most of the Psalms were written during the time of II Samuel". If so, what verification do we have of that?
Most of the Psalms were written by David, whose life is covered in II Samuel. Another author, Asaph, who wrote twelve of the Psalms, was a contemporary of David, "For in the days of David and Asaph of old there were chiefs of the singers, and songs of praise and thanksgiving to God" (Nehemiah 12:46). "Moreover King Hezekiah and the leaders commanded the Levites to sing praise to the LORD with the words of David and of Asaph the seer. So they sang praises with gladness, and they bowed their heads and worshiped" (II Chronicles 29:30). Thus most of the Psalms were written during the same time span covered by II Samuel.