Building a mob trap for spiders is a little bit different because they won't fall down that drowning hole. The blocks we're going to need for this trap are two buckets of water, some sand, some cactus, plenty of ladders, cobblestone, dirt, torches, glass, and a sign. Start by blocking off any exits so your spiders can't escape, and I'm going to replace the cobblestone around the spawner with dirt and put torches on the dirt to incapacitate the spawner. Put the torch back on and the same thing on this side.
So, now I just need to dig down two blocks, so I can go beneath the spawner. Dig out the entire room. Be sure to leave those dirt blocks with the torches on them, so the spawner is still incapacitated. All right, so finally, I have a room that's seven blocks wide, also seven blocks long, and two blocks underneath the spawner. I need it to be 12 blocks long, so I'm gonna count my way across. Seven, dig into the wall, eight, nine, ten, eleven, and twelve. I'll do the same thing on the other side, eight, nine, ten, eleven, and twelve. Now, just dig out all this stone.
I'm gonna place glass on this back spot here, eight blocks away from your back wall. Leave a small space for you to get through. Now, it's time to build an eternal spring by digging three blocks back and then those last two blocks down. Pull out your two water buckets, place them in opposite corners, and you've got an eternal spring. Pull water from it, and start lining this back wall with water. This is what will push your spiders into the trap. Just make sure you have one more bucket of water before you head back.
Your back room here, dig down one layer. right here where the water ends. This will be your collection trough. One block behind that, dig out every other block and replace it with sand and place cactus on top of that sand. These cactus are what's going to kill the spiders.
So, back in your spawning room, you're going to want to close up your eternal spring and get rid of these torches, the ones on the wall first, and then you can use your shovel to quickly get rid of the dirt and get out of here before the spiders spawn. Not quick enough.
So, there it is. The water pushes that spider into the cactus, and that hurts him until he dies. You can see he drops string right in that collection trough. Just place your last bucket of water in that corner there, and it'll push your string to a single collection point, and that's your string collection spot.
So, to get out, just dig your way straight up, and start placing torches and ladders. And there it is, the surface. You're going to want to place a sign, so you'll know in the future what this ladder leads to. So, let's head down and collect some string. I got kinda lazy and I didn't dig this out two blocks wide, so I can't fall, I just have to travel at the ladder speed, so I'll speed it up a little bit. And here we are. You can use this mob trap to collect all the string you'll ever need.