To dispose of the Qur'an, some claim it should be:
- Burned, or
- Wrapped in a clean piece of cloth and buried, or
- Disposed of in a flowing river.
Please give a reference to the Qur'an or Hadith regarding the correct methods of disposing the Qur'an.
When a Mushaf becomes unreadable, then there are two sayings for scholars in regards to what to do with it. The Hanafiyah and the Hanabalah say to bury it in dirt. While others, like the Malikiyah and the Shaf'iyah say burn it, following the example of Uthman (Radiyallahu Anh) as narrated in bukari, and mentioned in Abdullah Answer. Of the reasoning behind it, is so to avoid the text being walked on. So if you were to bury it, then bury it far away from where people walk, or normally walk, or burn it.
Also there is a third way mentioned by Ibn Unthaymeen, of using a shredder, where the papers of the Mushaf are to be shredded so that the form of a letter cannot be seen.
Primary Source: Islam QA
If the Mus-haf is no longer usable, it is permissible to bury them without burning, or burn and bury them away from dirt and footpaths so as to preserve them from desecration.
It is authentically reported in Sahih Al-Bukhari, under the chapter titled "Compiling the Qur’an", that Uthman ibn Affan (may Allah be pleased with him) ordered four of the best reciters among the Sahabah (Companions of the Prophet) to transcribe several copies of the Mus-haf (manuscript of the Qur’an), which was compiled into one manuscript by the command of Abu Bakr (may Allah be pleased with them). When they finished Uthman sent a copy of the transcribed Mus-haf to every territory. He also ordered that any other written records of the Qur’an be burnt. None among the Sahabah objected, except for what was reported that Ibn Mas'ud did. Yet, Ibn Mas‘ud objected to confining people to the Mus-haf that was sent by `Uthman to the territories, not to the burning process.
"Disposing" and "insulting" has a border between them. Our main problem is disposing without insulting.
For example, burning.
You see in the news, some enemies of Islam burn Quran for insulting it. They burn it to insult it. Their aim is to insult it by burning it. But that doesn't mean that burning something is always insulting it. You can burn it for disposing it as well. But, while burning it, you mustn't have the same intention with those how burn it for insulting. As long as your intention is just disposing it cleanly, why wouldn't you burn it?
In Islam, intention of doing something is as important as how you do it. If you do something normal with a bad intention, then your doing becomes bad. If you do a something normal with a good intention, then your doing becomes good.
If you are living in countryside, you can bury your old Quran in the ground as well. You can also send it to a paper-collecting factory for helping the nature by recycling old papers. There may also other good methods for disposing. There is nothing wrong with these solutions as long as you do them with good intention.
But please don't throw it in trash bin. When other people see Quran in there, they may think wrong things. If you really don't have any solution, put it into a black plastic or paper shopping bag, so people wouldn't know what is inside it.