(Excerpted from Kitzur Shulchan Aruch, Metsudah edition, translated by Rabbi Avrohom Davis, 134:3-4) In the following brief paragraph, observe how the author of the KSA – Rav Shlomo Ganzfried zt”l – cleverly and tactfully teaches us the halachos of kosher schach:
3) With regard to schach, there are also many halachos. Since it is our custom to cover the sukkah with branches of trees or with reeds; since they grow in the earth, and are detached from the soil, and do not absorb ritual impurity*, and are not tied together, you have no reason at all to hesitate using them!
*Footnote # 19 in the Artscroll edition: The halachos of which items become tamei (ritually impure) are complex. One of these halachos is that an item that can be considered a “utensil” is susceptible to tumah; an item that is not a utensil (such as branches and reeds) is not. It is prohibited to use a wooden shade made of slats of wood (even thin rods of wood) for schach, as these are susceptible to tumah (Igros Moshe O”C 1 #177). In general, when using mats (e.g. of wood or bamboo) for schach, halachic guidelines must be obtained. (Ed: The mats must be purchased from a reliable Judaic source which sells mats made expressly for schach.) According to Rav Moshe Feinstein (Ibid. O”C 5 #40.5). the custom is not to use as schach pre-cut wooden slats or planks that can be used for flooring or roofing (Ed. i.e. even if they are thin.)
4) Initially, you should be stringent, and avoid placing on the sukkah anything that absorbs ritual impurity to serve as a supporting beam for the schach, such as ladders which have in their side pieces holes in which the rungs are inserted; and certainly other utensils, such as a spade or a rake. Even placing them on top of the schach to reinforce it, should be avoided. However, if they are in place already, or you have nothing else to serve the purpose, all these are permitted, for we have an established rule that you are permitted to support the schach with something that absorbs ritual impurity.
MBY 630:1-13 Laws of walls (abridged)
(Excerpted from Kitzur Shulchan Aruch, Metsudah edition, translated by Rabbi Avrohom Davis, 134:2)
2) Concerning the walls of the sukkah, there are many different halachos, and not everyone is familiar with them. Therefore, you must make the walls full-length (complete) and strong, so that the wind cannot shake them or blow out the candles. (Footnote #4: This refers to a normal, usual wind. If the walls move to and fro because of the wind, they are not considered valid walls.) If you do not have enough lumber for four walls, it is better to make three complete walls than four incomplete ones. If you can afford it, it is a mitzvah to build a sukkah with a roof, that can open and close on hinges, so that you can close it when it rains, and when the rain is over, you can open it again. This way, the schach is kept dry, and you can fulfill the mitzvah of sukkah properly.
Footnote #16 in the Artscroll edition: “When the roof is connected with a hinge, it may be opened and closed on Shabbos and Yom Tov as well, and it is not subject to the prohibition against building and demolishing. One who wishes to use a plastic tarp to cover the sukkah should consult a halachic authority with regard to the proper method of connecting it in order to avoid these issues…” (Or, you can have a look at MBY 315:2 Making an ‘ohel’ (tent) on Shabbos (part 3)…!)