Quebecers often add something like a second “tu” when asking a question. For example:
T'as tu un crayon ?
I just don't know how to use it, like in what kind of expressions/sentences/questions? or if it depends on the region?
Joubarc is right, you don't actually need to; in fact, many Quebeckers don't use it in formal situations (though I have never met one who does not use it otherwise). Of course, it should never be used in most texts.
If you do wish to use it for any reason, this “tu” actually replaces “est-ce que”, but is placed after the conjugated verb. You can use it with other pronouns as well, for example:
Small addition, which, considering Kareen's comment, may be regional: we do actually use the “tu” with "vous"; there are two ways to do so:
Like Joubarc mentioned, there is no need or convention about this way of speaking. I could maybe compare it to some people saying y'all in English.
As far as I know, this construction seems like the amalgamation of the two ways of asking questions in the second person singular:
Put them together and you get "Tu as-tu un crayon?", which, when ellipted, gives us the "T'as-tu" structure. It is used with just about any verb and is usually used when asking questions. It can be used with most pronouns, though it is informal speech, so I've rarely ever used or heard it used with nous or vous, as those are usually a little more formally in Québec. Interestingly enough, when used with pronouns other the second person singular, the second pronoun remains "tu". It usually follows this construction:
1st person singular: J'ai-tu?; J'veux-tu?; J'mange-tu?; etc.
Again, it's a way of speaking in informal situations, and it is absolutely not necessary to employ it. You will be perfectly understood even if you don't use this rather particular structure.