I'll just add two ways I determine this:

1 - Look at them in the light, check out the reflections, and look for any discoloration. There will be a darkening in the areas that you commonly play, as opposed to areas you don't ever touch. The oils in our hands will leave behind residue and corode the strings.

2 - I am so accustomed to the sound of strings that I can easily judge their newness immediately, after 30 years of playing.

Over time your ear will get used to what fresh strings sound like and what your own tastes are. You'll just know.

We ALMOST ALWAYS change to completely fresh strings before shooting a GuitarTricks tutorial. Some instructors like to have them on a few days to find their own sweet spot.

I am an EXTREME case but when I am recording an album or anything very important I change strings at the very least every other day on my electric. I am crazy about bright strings! I can hear a big difference even after 3 hours of playing. But that's my own personal quirk and taste. Other people would not agree. :)

-Carl.