William, that's a preety hard question to answer, but i'll try to do my best,so:
Those tables look very accurate http://www.russianlessons.net/grammar/pronouns.php. As well as those ones http://russianlearn.com/grammar/category/possessive_pronouns.
It's pretty clear that the stadndard usage of those posessive pronouns will be:
Когда ты отдашь мне мою книгу?
Я скоро отдам тебе твою книгу.
Когда ты отдашь ей ее книгу?
Когда ты отдашь ему его книгу?
Нам нужна наша книга.
Вам нужна ваша книга?
And so on.
And it gets harder with "one's own". As I would imagine, it's more for generalizing, say:
Каждому нужна своя книга. (everybody needs his/her book)
BUT. NOT EXACTLY GENERALIZING. And this fact made me think that's gonna be hard to explain that.
I've come up with the thought that we tend to use "свой" in imperatives
E.G.
Подними свою руку!
Подними свои руки.
Забери свою книгу.
Иди к своему профессору! (we can say this way if we are irritated (for example if the person quotes the professor too often or anything) So it definitely has to do with emphasis
Напишите свой адрес.
Расскажите о своем брате. (but we can also say "о вашем брате") Bearing in mind the examples from your book, I'd say that accosding to the rule, it is more correct to say "вашем".
While you can never say under any sircumstances Расскажи о твоем брате. It is just plain wrong. So it is gonna be:
Расскажи о своем брате.
Then the next thing I'd like to pay your attention to will be the examples of the usage of possessive pronouns with the members of the family, and, say, with a word "professor" (I just decided to use this word because it is used in your textbook) So, now I'll try to provide you with examples of the usage of the words "a sister" and "a professor"
Statements (со местоимениями "моя" и "своя"): Это моя сестра. Я люблю свою сестру. Я люблю нашу сестру (if it matters that there are some other siblins). Расскажи о моей сестре. Моя сестра ему нравится.
Questions (с местоимениями "твоя" и "своя") : Это твоя сестра? Ты любишь свою сестру? Ты любишь вашу сестру? Что бы ты мог сказать о своей сестре? Как думаешь, ему нравится твоя сестра?
I sould say that looking at what I wrote above I'm like "What the hell, there's no logic"
I mean posessive pronouns are soooo semantically tricky.
But definitely I know where to use which and there's what I think:
If you want to ask somebody about a person or an object that either is related to him/her or belongs to him/her, you use "свой"
Раскажи о своем велосипеде.
Расскажи о своем брате.
Расскажи о своей книге.
BUT.
Расскажи о вашем профессоре. (because he/she teaches not only you, typically there's a group)
Расскажите о вашей книге (because it's a polite form so you use plural) (or because you're asking several people)
And so I can infer that свой is typically not used when you ask several people about the people related to them or the thing belonging to them.
And that looks like the answer to your question.
NOW ABOUT "РАССКАЖИ О МОЕЙ СЕСТРЕ"
That seems pretty logic. because if you say "расскажи о своей сестре" that would mean "tell about your sister"
NOW ABOUT "ЭТО ТВОЯ СЕСТРА?" you can't ask "Это своя сестра?" cause that sounds conpletely illogic. But we do have a question "Это свои?" When for example you're at war and so you have "your men" and "not your men" who are "свои" и "чужие" respectively.
So now let's talk about a professor
a professor typically gives lectures to several people, as I've mentioned above and so it is preferable to say "ваш", because if you say "расскажи о своем профессоре" that makes sense, but saying so you ignore the fact that he/she teaches other people as well (but it's ok to say so as I presume)
So the examples would be
statements: Наш профессор читает интересные лекции. Наш профессор хорошо преподает. Наш профессор ценит своих студентов.
questions: Вы не могли бы расскать о вашем профессоре? Ваш профессор хорошо преподает? Ваш профессор ценит своих студентов?
You can probably ask why not "его студентов".
We can certainly use "его студентов" but in another context.
We'll say
Он любит своих студентов.
Я люблю свою сестру.
Он любит свою сестру.
But if we word the sentence differently, we use "его, ее, мою..."
Его студентов обокрали. (кто-то обокрал)
Мою сестру преследуют (кто-то преследует мою сестру)
Иван любит его сестру.
By the way, it's ok to say "Иван любит его сестру" when talking about someone else's sister, it would be translated "Ivan loves his(someone else's sister). But if you say "Иван любит свою сестру" that means that "Ivan loves his(his own) sister
I really hope that helps
После уроков мы ходили в лабораторию к профессору. В воскресенье мы поедем к друзьям. Мы уже звонили им и сказали об этом.