Spiders appear in level 266
Some spiders are already sitting in nests, and on some levels you have empty nests for the spider to jump into.
The trick to removing a spider is not as hard as it looks. You see the crops that are covered in webs? These can be broken by matching crops with the webbed crop. So in this image, moving the strawberry over to form a row, will break those webbed strawberries. Make another match to remove them and the spider will be moved too. You just need to make a clean row match next to him.
You can see how to do this in action here
https://youtu.be/P1fdHC3VlGg