What's the best time of year And how would you cut a leggy chinese evergreen into stems for re-rooting? Would you use something to promote rooting after cutting?

Welcome to ATP,
Do you know the botanical name of your plant? Is it a Aglaonema?

One thing I learned is to not root the cuttings in water. Sure, the cuttings will root okay in water, but the roots may be too weak to make the transition to being planted in soil. Best to take the cuttings, use rooting hormone (optional), stick the cuttings in a decent medium and keep moist.

Here is a link which has good instructions.
http://www.jaycjayc.com/propag...

Edited to add link to Aglaonema in the ATP database:
http://garden.org/plants/brows...

Hi & welcome! Summertime seems to be the best time, but have done it when bored during the winter too. With a plant like yours, with multiple stems, you could cut one now, another when that has taken root, then another, so it never looks like it just got a drastic haircut. When you cut off the top part, the stump will grow one or more new tops. I've been doing them for decades, never used any hormone, just stick in a pot. The more length of stem I bury, the better the success seems to be. Just don't stick it so deep that the petioles (leaf-stems) are under.

I submerged about 8" of this stem and a new stem grew from every node. (A. modestum, specifically.)