Spiders have special claws in small size, which allows taking the strands of the spider web. Some spiders have two or three claws on the end of each leg. In this way, the spider can move quickly through the net without being trapped.
In making a net, one of the claws has a special area that is used to hook the net strands. Spiders can use special claws to swing from threads to other strands without having to touch the sticky part of the net. Therefore when the spider touches the net, it is not like a fly with large wings trapped in a strand of sticky nets.
The point is the contact of the spider on the net is very small. Even when touching a sticky web, the amount of glue that is touched is very small and therefore easy to remove.