Re: What's the correct way to use 's with the meaning of possession?
Welcome to Using English.
Your question is more complicated than you might think.
The -ing words are a combination of a verb and a noun. Speaking, driving, telling, etc.
Under strict rules of grammar, the possessive is needed. I'm angry about his telling you. I'm angry about Mark's telling you.
However, this "rule" is often not followed. I'm angry about him telling you. I'm angry about Mark telling you. In fact, most people would tell you that "Mark's telling you" looks funny.
If the subject is the action itself, then you need the possessive: Mark's driving scares the bejeesus out of me.
If you want to try a few full sentences, we can tell you that it's required or it's optional under the rules of common use, if not the rules of strict grammar.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.