I'm just growing herbs for the first time. When snipping chives, do I snip
an inch or so at once from the entire growth, or do I clip the individual
chive stem down to the base?


Either method can work. If you clip the individual chive stem, leave about
1" remaining above the soil level. This is my preferred method as the plant
will replace the removed stem with a fresh one, and I think the appearance is
better afterward.

Regards.