This spider just crawled into my house when I opened the door. It was black, medium-sized, pincers and it had a small orange triangle on its back. It crawled somewhere under the couch before I could get it outside. What do I do now without killing it?

If you want to kill it bug spray will help

or

catch it and name it as Tobby , you can keep him inside a proper ventilated glass cage , but don't forget to feed him

It's Not A Black Widow.. Is It? Move The Couch. Grab A Large Tall Glass Or Cup  Then A Ruler With  Your Other Hand.. Ease It Into The Glass.. Cover The Glass
With A Plate You Have Gotten And Carry It Out Side.. Black Widow Is Nasty.. Do  Not Touch Nasty Painful Bite

I was going to say sleep on it.the answer will come one way or another . :) ...most spiders can not kill a human unless allergic to it.....buy a cat to kill the spider(then no moral question comes into play) then you won't have to kill it.then get a dog to kill the cat ,then make the dog your best friend. : )

Don't recall any sider with pinchers, fangs yes, pinchers, no.  If your're referring to the first set of legs nearest the head those are the pedipaps.  Sort of touchie, feelie, tastie appendages as well as legs. If it was a shiney black spider with a large abdomen, chances are that it's a Black Widow and you DON'T want and or need her as a roomie.
Spray deodorant or hair spray, even a shot of PAM will take care of her.
Even then, don't touch.  Black Widow bites very painful and can be fatal. I wouldn't trust a wad of TP or even a paper towel to remover her.  Unless you squish her throughly, use a piece of cardboard to scoop her up.  She may not be (quite) as dead as she looks and if you Google a picture of them, you'll see her fangs are impressive.

Well! This is a conundrum, as there are many species of Spiders. However if I were you, I would not touch it , but rather get it into something, and then try to find out what it is, if you are interested.  Google it w/ description.

Don't recall any sider with pinchers, fangs yes, pinchers, no.  If your're referring to the first set of legs nearest the head those are the pedipaps.  Sort of touchie, feelie, tastie appendages as well as legs. If it was a shiney black spider with a large abdomen, chances are that it's a Black Widow and you DON'T want and or need her as a roomie.
Spray deodorant or hair spray, even a direct shot of PAM will take care of her.
Even then, don't touch.  Black Widow bites very painful and can be fatal. I wouldn't trust a wad of TP or even a paper towel to remover her.  Unless you squish her throughly, use a piece of cardboard to scoop her up.  She may not be (quite) as dead as she looks and if you Google a picture of them, you'll see her fangs are impressive.
If you can't find her, drag out your vacume cleaner and go over the couch, between &
under seat cushions,  even the couch underside if you can...any little dark place where she could be.  After that, keep an eye open for what looks like an explosion in a spider web  factory.  Black Widow 'webs' are little more than a bunch of silk strands going every which way.  She's a messy house-keeper as well as a nasty neighbor.

KILL IT!