clutch cable repair

I have a 1987 Acura Integra, 167k miles, still in good running order

I was driving to my classes today when I noticed the steering, shifter
and clutch were a little stiff. This is common where I live as it is
quite cold this time of year. I thought nothing of it until I got to
the end of the street I live on and the clutch pedal gave way and
slammed all the way to the floor as I tried to shift back into
neutral. I managed to get it back in my garage and have looked at the
pedal and the pedal seems to be fine but my next guess is that the
clutch cable gave out.

I'm not really sure how to go about replacing this cable so any info
you can give me would be of great help