:wasalam:
they may be destroyed by burning or by cutting them up so that the verses of the Qur’aan and the name of Allaah disappear, or they may be buried. Putting them in a shredder probably the easiest if you have access to one. Of burn them in your backyard. If you don't have those options then cut them up.
inshallah You can throw it away after shredding. The whole purpose is so the letters don't make a word, and when shred up they are nothing more than individual letters.