In junior high, my favorite English teacher was Mrs. Webb. She was not only a good teacher, she was also a good person, helping me through some rough times in early adolescence. Much of my "good grammar" was the result of her teachings. A good example is the previous sentence's use of the possessive pronoun before a gerund.
Many of the examples I can give, however, are considered "classic grammar," or "antiquated grammar," as they are older rules that have fallen out of common usage by the growth and transformation of the American English language. The biggest of these antiquated grammar rules seems to be the use of male possessive pronouns when referring to a group of people.
When using possessive pronouns, you want the pronoun to match the number and gender of the noun it references. The number matching part of that possessive pronoun select rule often confuses people.
If you are referring to individual items owned by the individuals of the group, for example, the singular possessive pronoun should be used.
The ownership of a specific item:
Each of the participants shook his head.
versus the group's ownership of the many items:
The participants shook their heads.
The use of the "his" in this particular case indicates the group of people contains at least one man. "His" is used when referring to individual items owned by the individuals of the group if the group contains one man. If, and only if, there are no men in the group, "hers" can be used. This rule means you can have 99,999 women and one man in a group, but you'll still (antiquated grammar speaking) use "his" and not "hers."
Apparently, this is not politically correct in this (post-)feminist era. Instead, "better" grammar is to ignore the noun's number, and use the gender neutral plural possessive pronoun "their" in both cases:
Each of the participants shook their head.
Personally, I disagree with this venacular use of the gender-neutral plural possessive, and continue to use "his" to indicate singular possession.
To me, "his" is as gender neutral as "their."