Catch it. Then destroy it. Then hunt the rest of my building and destroy any other spiders I found.
Destroy as in, I'd crush it. Crush it into paste. Not just step on it once, but grind it under my boot heel until there was nothing measurably solid left (little piece of leg still sticking out? More crushing and grinding). Then I'd douse it with lighter fluid and hit it with a match until it burned out. And the remains, I'd mop up with tissue and flush.
I can see the headlines now...
..."In other news, a New England apartment complex burns to the ground after a tenant went on a spider killing spree throughout his building, allegedly grinding the spider and then dousing it with lighter fluid and watching them burn."
