Vertical files are odd beasts, and may contain any number of types or formats of material. In that regard, they can be similar to manuscript collections, just on a smaller scale. The first thing you will need to do is distinguish between published material in a vertical file (such as a newspaper article) and unpublished material (such as a a typewritten draft of a speech).
If the item is published, you will follow whatever rules your citation style requires for that type of published material, followed by some additional information about the vertical file location:
[Regular citation]. In the [Name of vertical file] vertical file, Special Collections, Augustana College, Rock Island, Illinois.
Example 1: An article published in Rolling Stone magazine that you found in a vertical file in Special Collections.
Sager, Mike. "Gut Check in the Heartland." Rolling Stone 7 Jan. 1993: 30-31, 54. In the Augustana College Football-1993 vertical file, Special Collections, Augustana College, Rock Island, Illinois.
If the item is unpublished, you should use the following format:
[Title], [Date], in the [Name of vertical file] vertical file, Special Collections, Augustana College, Rock Island, Illinois.
Example 2: An unpublished, undated draft of an essay found in a vertical file
"How Large Is a Small College", undated, in the Bergendoff, Conrad John Immanuel-Articles by-no date vertical file, Special Collections, Augustana College, Rock Island, Illinois.