This is the device that made so much of what we take for granted today possible. Virtually every bridge (large ones at least), every tall building older than 30 years (and receding -- I'm dating myself), and most major engineering undertakings more than a couple of decades old were designed by people assisted by these devices.
They're actually very simple machines comprised, mechanically, of a sliding member contained betwixt two stationary members, surrounded, in turn, by a movable transparent piece, upon which is inscribed a single vertical line, called a cursor.
Slide rules operate by using logarithms, where multiplication is accomplished by adding the logs of two numbers, then taking the anti-log of the result. It's a simple and elegant system. Most slide rules did much more than simple multiplication and division; the vast majority of them were able to perform trigonometric, square, cube, and circular (pi-based) operations.
For an excellent on-line treatise on slide rules, check out Gordon Smith's slide rule home page . Andrew Davie also has a wonderful slide rule site in Oz known as The Slide Rule Trading Post . Both are worth a visit.
The scales on the front are (from top to bottom) K, A, DF, CF, T, S, CI, C, D, and L. The CF, T, S, CI, and C scales are carried on the sliding member.
The reverse carries a lengthy list of conversion formulae and the correct setting for each.
By the way; I know how to use it, too. The batteries have yet to die on me....