What determines whether a document needs to go to genizah (shemos).
Does it have to have Shem Hashem? Or does it apply to other documents as well? What about sedrah sheets and other Torah related material (such as your weekly sheet on the parsha) which may not have the name of Hashem but which discuss Torah matters? How should they be disposed of?
In Torah law, the obligation is only to put documents with the name of Hashem into genizah. The Sages added that even divrei Torah require genizah.
Some write that a Torah sheet that was written for one-time use does not require genizah (see Netziv, Meishiv Davar 2:80, and see also Iggros Moshe, Orach Chaim 4:39, concerning a sefer that is no longer used for Torah study; Rav Moshe writes that his chiddush is contingent on the agreement of poskim in Eretz Yisrael, who did not concur with the ruling).
Another reason for leniency is the fact that sheets are printed and not written; although many poskim are stringent concerning printed material, some argue that modern non-mechanical printing methods provide greater room for leniency.
The general custom for Torah sheets is to be stringent, and it is right to act this way, although some are lenient (see Shraga Ha-Meir 5:61:1).
Even for those who are lenient, it is certainly forbidden to act disrespectfully with the divrei Torah, and one must be careful to dispose of them in a respectful manner — by wrapping it in a plastic bag, and disposing of it.