What should one do who finds a booklet discarded on the ground that contains Quranic verses or one of the names of Allah the Almighty, and has picked it up?

The one who picked up the paper did well, and he should dispose of it according to its condition. If its owner can be identified, then it is a lost item (Luqata) that must be announced. If not, then he may benefit from it, or dispose of it by burning it, or by soaking it and burying it, or by shredding it with a shredding machine.