How should one dispose of secular newspapers and magazines that contain Divine names (e.g., "G-d" [completely spelled] and/or the transliteration of the Tetragrammaton)?

If you have seen G-d’s name in a newspaper, the paper can still be thrown away in the garbage but not in a way that shows scorn or derision (don’t put it next to liquid or smelly garbage; throw it out with other papers). You needn’t worry about there being G-d’s name in the paper unless you have actually seen it there (Shach Yoreh Deah 179,11; Mishna Berura 85 10; Shu”t Iggrot Moshe Yoreh Deah I 172-173).