How can you tell when a clutch is dying?

I only recently starting driving manual so not too sure how to tell but I did notice a difference from driving a new car, with its clutch being 'touchy', to my car's clutch not having to push on the pedal as deep...

Also I notice that when I shift from 1st to 2nd in my car the shifting is a bit jerky - is that also a sign of a dying clutch?