Actually, this one's pretty easy to cover. It has more to do with clarity than with grammar, though there's a bit of grammar involved, too.
Here it is: A misplaced pronoun causes confusion. That is, the random use of "he" or "she" or "they" when the reader has no idea who he, she, or they might be.
Pronouns always have what's called an antecedent. An antecedent is that which comes before. So the antecedent is the word (usually a proper noun) that comes before the subsequent pronouns that refer to it.
Deborah burst through the door. She realized at once she was in the wrong bathroom.
Deborah is the antecedent for both uses of she above. Without the "Deborah" in the first sentence, we would not know who "she" was.
Note that the antecedent is not necessarily found in the same sentence as the pronouns that refer to it.
Pretty clear, right? Things start to get muddy, though, when there are more than one character in a scene, and the hes and shes begin to proliferate. That's when we have to be especially careful with pronoun placement.
Maria stared at the woman on the porch. She raised her hand to her left nostril in the ancient greeting, hoping she would understand.
In the above, there are two antecedents: Maria and the woman. When we get to the second sentence, we don't know if the first "she" refers to Maria or to the woman. Which one is raising her hand to her left nostril? And then, of course, we don't know to whom the second "she" is referring, either. The entire thing is unclear.
In this instance, rewriting is probably your best option, because you don't ever want to start two sentences in a row with the same word:
Maria stared at the woman on the porch. Maria raised her hand to her.... (You see my point.)
Maria stared at the woman on the porch while raising her hand to her left nostril in the ancient greeting. She hoped the woman would understand.
Another tricky business is dialogue tags. There are times when "he" or "she" can be perfectly clear. There are other times, however, when we may not know who is actually speaking. So be careful with that.
It comes down to asking yourself, "Am I being clear?" It's easy to forget, sometimes, that we know EXACTLY who we're talking about, but the reader does not. So be extra careful in the placement of your pronouns, and extra picky when you go back to edit your work. Any time you've got a sentence with only pronouns in it, go back and FIND THE ANTECEDENT. Does it come DIRECTLY BEFORE the pronoun? (Note: That doesn't mean it the word right in front. It means the NOUN or PROPER NOUN directly before the pronoun.) If it doesn't, your pronoun reference is most likely unclear.