Shoot it with a rubber band.
Finding a rubber band
Rubber bands can be found near a postal drop box. These boxes are for the postal service to store mail so the delivery person does not need an automobile. Mail is typically bound with rubber bands, and delivery people tend to discard the bands on the ground.
Shooting a rubber band
Hold one hand as though you were pointing at something with your index finger. Hold a rubber band in the other. Prop the rubber band on the index finger of the hand that is pointing. Pull back on the rubber band. Letting go of the rubber band should send it flying in the general direction that you are pointing.
Approaching the beast
It is probable that a spider that is not moving will not move unless it is bothered. Your approach should be soft enough to not cause any sudden vibrations, slow enough to not cause much wind, and from a direction that will not cast a shadow on the spider.
Actually killing the thing
Arm the rubber band and approach your target. Each step closer increases your killing chance, but also that you disturb your prey. Steady now.
If you shoot a rubber band at a spider from the distance of a foot, you will probably be successful.