How to save spaghetti squash?
I haven't specifically tried to save that variety of squash, but I've had good luck in general holding other varieties of winter squash for a few days by halving, sealing the cut side, and then refrigerating for.  A few notes:


If you have a large enough knife, just make a single cut through it.
Either place it cut-side down on an appropriately sized dish with a flat bottom (eg, a casserole dish), or cover the cut side with plastic wrap ... (of plastic wrap, then set in the dish, so you don't accidentally knock off the plastic wrap in the next couple of days).


When it comes time to use the remaining half, if the cut surface is dry, shave a little off.  Clean out the seed cavity when you're finally going to use it.  (this allows you to scrape back down to moist flesh, and reduce evaporative loss)

How long you can hold it will likely be affected by things like how often you open your frdge. I've never tried putting in the crisper after wrapping (as I tend to have too much stuff in there already).

If you're looking to get the longest possible strands out of the squash, I think to need to cut it from stem to blossom end ... but that would increase the cut surface area.  If that isn't a goal, it's probably better to cut it across the stem-blossom axis.