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:
1- Formal: Verb+subject+object? eg. As-tu un crayon?
2- Informal: Subject+verb+object? eg. Tu as un crayon?

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.
2nd person singular: T’as-tu?; Tu veux-tu?; Tu manges-tu?; etc.
3rd person singular: Il a-tu? Elle a-tu? On a-tu?; Il veut-tu? Elle veut-tu? On veut-tu?; Il mange-tu? Elle mange-tu? On mange-tu?; etc.
1st person plural: N/A
2nd person plural: N/A
3rd person plural: Ils ont-tu? Elles ont-tu?; Ils veulent-tu? Elles veulent-tu?; Ils mangent-tu? Elles mangent-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.

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:

Elle a-tu dit oui? (Est-ce qu’elle a dit oui?)
J’ai-tu quelque chose sur mon nez? (Est-ce que j’ai quelque chose sur mon nez?)
On y va-tu? (Est-ce que nous y allons? Never use this “tu” with “nous”.)
Ça va-tu? (Est-ce que ça va?)

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:

• The “tu” is changed to “vous”, granted this is rarer. Example:

  Vous voulez-vous aller au marché?

  This is sometimes taken to extremes and the “tu” is also added! Example:

  Vous voulez-vous-tu aller au marché?

• Then, of course:

  Vous voulez-tu aller au marché?

It is an English-ism and does come from replacing the “Est-ce que”

T`as tu un crayon?
(you have your(yourself) a pencil?)
Do you have a pencil?

As a Québécois, I would ask you to not use it. It is nowhere near “le bon usage”. It is not taught in school and I hope it disappears as soon as possible.

In fact, in questions, the word ‘tu’ is a phonetic variant of the old French ‘t’y’. Ex: Tu veux-tu? (Tu veux-t’y?) This was lost in France but is still used everyday in Quebec in non formal conversations.