Rather than trying to reconstruct all of the information available about fairly recent experiments concerning your very question, please take the time to read this comprehensive but understandable discussion:
Spiders have little hooks on their feet, a bit like fine velcro, which enables them to climb (and stick to ceilings!). You obviously won't see or feel them on a small spider, but on a large one, like a tarantula, if you stroke its feet, they feel like fuzzy felt (if anyone else is old enough to remember that!!).