Images not Sharp Enough

[DacrimL]

Ok have been reading some info from a reputable photo magazine as to why some images are not sharp. Their #1 point was to do with shutter speed and I quote -

In the days of film photography there was a general rule that in order to get sharp images from a hand-held camera the shutter speed needed to be at least one second divided by the focal length of the lens.So if you were shooting with a 100mm optic the shutter speed needed to be at least 1/100sec, which because of the way shutter speed is set usually translates to a setting of 1/125sec or faster.
This rule still holds today, but it is somewhat complicated by the focal length magnification factors of sub-full-frame sensors and image stabilisation systems.
For example, if a 100mm lens is mounted on a Nikon APS-C format SLR like the D5200, which has a focal length magnification factor of 1.5x, the photographer would need to set a shutter speed of at least 1/150sec.
Canon APS-C format DSLRs like the EOS 650D have a 1.6x focal length magnification factor, so the shutter speed would need to be at least 1/160sec.

Will post link to article if that is allowed.

Basically my question is how does one know what the focal length magnification should be for ones individual camera and how does the conversion equation work. So far I have sort of been guessing what shutter speed to use relative to which lens I am using or am I just making things too difficult for myself?