Tank-slappers are complicated to describe, but are basically caused when the motorcycle's steering is knocked out of line. But rather than correcting it-self back into line, the momentum of the steering assembly carries it past where it need to be and actually turns it he other way. The process repeats the other way and becomes more severe – eventually causing the rider to lose control.
It's the job of the steering damper to stop this from happening while still allowing the steering to move freely in normal conditions. That's the main reason why steering dampers are now hydraulic. In the past some manufacturers used friction to slow the steering down, but there were two problems with that. First, the steering damper slowed the steering down all the time which did nothing for the motorcycle's handling. And second, although the friction was high, it wasn't high enough to stop a really bad slapper.
Now steering dampers are hydraulic just like suspension dampers, meaning the faster your try to move the steering, the more resistance the steering damper will offer. So your steering remains responsive at low speeds, but if a tank slapper does start, the steering damper resistance gets stronger as it gets stronger. Inside a steering damper there isn't a lot going on. The steering damper generally comprise of an outer body, damper rod or vane in the middle, some form of adjuster and an expansion circuit. When fitted, oil is pushed around a circuit in the body and through a valve. The adjuster normally moves a needle in or out of the valve and adjusts the resistance it offers to the oil.
In terms of mounting position, there's not much in it. Yoke mounted steering dampers are easier to adjust and offer a more liner response than straight mounted steering dampers because each degree of steering displacement the amount of oil in the damper – however they make it harder to remove the yoke and not everyone likes the look. Conventionally mounted steering dampers are not linear. They convert rotary to linear motion; meaning the movement to oil-displacement ratio is lowest when the damper is at 90º to the steering movement.
However, this effect is so small it doesn't make much difference in use. The same can be said for mounting down the side or across the front of the motorcycle. As long as the steering damper generates enough force to control a tank slapper it makes little difference how this is done – although from a weight and space point of view mounting across the motorcycle is more beneficial.