Tips: don't use a broom, it will just run away into a safe hiding spot.
It's not much use now but for next time..... On Amazon you can get a spider catcher, I got one for my sister when she got her new house as she panics and something like a spider would have her in a right frenzy! She likes the spider catcher!
Take the tapestry down, shake it out, kill the spider.
Ok, so I am deathly afraid of spiders, they scare the sh*t out of me even though I know I'm huge compared to them. But on my ceiling I have a tapestry and I found a medium sized spider in the corner of it with a web. I didn't mess with it all day and noticed it was kind of moving around. Suddenly I decided I would not be able to sleep with it directly above me so I tried killing it. It was so hidden I can't be sure it's dead so it might be inside the hanging tapestry. I'm worried that if it is in there long enough, will it hatch eggs? What do I do? It's a legit phobia of mine so this really freaks me out. I'm not even sure it's alive but I'm to afraid to check.