Easy: just take some parts from a Lego Mindstorms kit with some plastic parts.
The legs are from a locomotion concept by Klann Linkage.
They work in pairs by converting the rotational force of the motor into movement on both legs.
Four gears in all make the eight legs move forward.
This is a companion discussion topic for the original entry at https://community.robotshop.com/blog/show/how-to-make-a-lego-robot-spider