24/7 as long as you don't mind the noise IMO
. Your skimmer is your main source of waste removal and is a vital part of keeping your water clean/healthy.
Having said that I personally do not run my skimmer 24/7 because I don't like the noise after work while I'm trying to relax and my tank doesn't suffer in the slightest from not running it 24/7.
NOT running a skimmer 24/7 does not hurt the skimmer (it will still work fine IME) but of course if you have trouble keeping your tank's water perfect then I would highly recommend running it 24/7.
My skimmer's set on a timer to run from 10 PM to 4PM (18 hours) so I have nothing but the sump pump to hear after work which is virtually silent.