Stain, poly, cut… What order should I use when installing window trim?
I usually stain &amp; poly the pieces, cut to size, stain the exposed end-grain, install, putty, then one more coat of poly.

So...
Stain -> Poly -> Cut -> Stain -> Install -> Putty -> Poly

Staining &amp; poly before you cut makes sense when you're doing alot of trim - you can fit alot more material on your saw horses when its in 10' pieces.  But if you're just doing one window it probably doesn't matter.  Staining the ends again after the cut helps them to not stand out if your joints aren't perfect.  And the final coat of poly after everything is done helps the putty and other dings, imperfections, etc. that may accumulate during the install to not stand out so much.

And as Chris C points out - lots of sanding.