Here's my guess:
https://en.wikipedia.org/wiki/Argiope_aurantia Were there any colors that you noticed?
It's probably just looking for a warm bed for the winter. If it's a garden spider (above) it's also not really a threat to your or your family, and will want to go back outside for food in the spring.
I am a spider pacifist / recognize their value in pest control, so I just shoo them out. My typical trick is to use a paper towel--don't press down on them, or they will squish. But rather, fold it up so it makes a pocket--they are looking for corners to hide in. It will settle down (or you can close up the open end of the pocket, and it will) and you can just put the paper towel outside.
If you don't want to engage that closely, use something with a handle: broom, shovel, etc. give it a "lid" and again, likely to settle / cower in the "corner" while you transport it.
If you have to try something to get rid of insects, you could also look at diatomaceous earth. Food grade DE is safe for pets. If the spider is really that big, I'm not sure how effective it would be, though.