Use the adjective araneidan to describe something that's spider-like. You could, for example, describe a modern dancer's strange, araneidan movements across the floor.
When something looks or acts like a spider, it's araneidan. The eight-legged title character in "Charlotte's Web" is araneidan, and the hand movements accompanying the children's song "The Itsy Bitsy Spider" are also araneidan. You can call a spider an araneid, too: both the noun and the verb come from the Latin root aranea, or "spider."