In an introductory note to this chapter, the Kitzur Shulchan Aruch writes that most Jews are already familiar with the prohibited labors of Shabbos and that he is only addressing common situations with which people may not be familiar. Clearly, the laws of Shabbos constitute an area requiring much greater study than this email alone will allow.
80:17 One may not strain liquids on Shabbos because there are many laws involved. One may drink through a cloth because borer only applies when preparing a food or beverage before partaking of it. In the case of drinking through a cloth, all he is doing is blocking the undesirable matter so that it doesn’t go in his mouth. Some authorities prohibit drinking water through a cloth because there’s an aspect of laundering involved. One may be lenient in a case of great need if there is no clean drinking water. One may not, however, drink through his shirt sleeve, because of the likelihood that he would wring it out afterwards. (Filtering already-drinkable water does not pose a problem of borer – OC 319:10. The situation involving copepods in New York City tap water is beyond our scope; consult your own rabbi for guidance.)
80:18 If a cup of coffee has grounds at the bottom, or if another beverage has dregs, one must be careful not to spill out all of the clear liquid. Rather, some liquid must be left behind with the undersirable part. (One may pour it all out if he’s going to drink it immediately - Mishnah Brurah 319:55.) If milk separates, one may only remove the butterfat that is needed for immediate use. One must be careful not to remove all of it; some must be left on the remaining liquid. (The converse is also true; if one wants to take the liquid part, he must leave some with the remaining fat – MB 319:62 .)