Sheimot/sheimos are written items with:

• God's name in Hebrew or even in other languages;
• Three consecutive words of Torah in Hebrew (or commentaries on the Torah in any language); or

• Halacha in any language.

 

These holy writings (tashmishei kedusha) may not be thrown directly into the trash, but should ideally be buried with like items (sheimot):

• Holy writings that contain God's name.
• Parts of Tanach (24-book Jewish Bible).
• Explanations of the Torah or commandments.

However, if a printed or written page (in contrast to parchment scrolls such as tefilin, Torahs, or mezuzas) contains God's name plus secular content, it must be double wrapped in plastic before being thrown in the trash.
Do not throw into trash, even if double wrapped:

• Handwritten scrolls of Torah, tefilin, mezuza.
• Printed Torah, Talmud, siddur, books of halacha, or Torah commentaries.

Rather, put them into a sheimot collection box or wrap in plastic and bury in a place where they will not be dug up. It does not need to be a cemetery.

Double wrap and throw into trash:

• Newspapers and flyers that have Torah psukim or Torah commentaries and also have non-Torah content.
  Reason Non-Torah material should not be buried as sheimot. 
• Children's school handouts with psukim from the Torah or halachot that also contain non-Torah content (if they ONLY contain words of Torah, they should be buried as sheimot).

For disposal of items used for mitzvot (tashmishei mitzva), you may wrap in one layer of plastic and throw it in normal garbage:

• Lulav,
• Etrog, or
• Talit/tzitzit (but NOT tefilin!)