I am just learning Italian and my Italian teacher told me that you should you use the formal "scusa" when talking to those you don't know, which will be everyone when I go to Italy! However, in the text book I am using (my class is finished now), and on several internet sites, it uses "scusi " in restaurants and stores. I don't want to insult anyone when I am there. I want to be correct. Is it safe to use "scusi " and the " tu " form with everyone or should I be sticking to " scusa " and the " voi " form?

Grazie!

Perhaps you misheard your teacher?

Scusi is the formal form; scusa is the informal form.
http://www.garzantilinguistica.it/verbi_ita.html

You should be using the formal, which would be scusi, and never addressing anyone you don't know as tu.

I hear Italians saying permisso when they want to get past you, so I guess scusi means about the same thing? I always say scusi and they say permisso.

This used to really confuse me because I had assumed that the -i form was informal, But I layer learnt that as it is an instruction, so the "imperativo" form applies - So "Scusi".

Oh please! Scusi and permesso (NOT permisso) are not even similar. Permesso is exclusively used when, as you said, you want to go past somebody. Scusi simply means "excuse me" in every other situation, and as others said, scusi (formal) is related to Lei (NOT voi), and scusa (informal) to tu.
On the other hand, it wouldn't be correct to assume that Italians address everybody they don't know the formal way; in fact, they can be very very informal, and you'll hear many Italians address yourself as tu. It's a matter of social rank and age, above all, and requires pretty much knowledge of Italian every-day culture, and intuition. Of course, addressing everybody as Lei means staying on the safe side, so that's actually what you should do as long as you're not acquainted with the Italian way of life...
Please note also that voi has really nothing to do with scusi (nor scusa, of course). Voi is plural (informal, but in every-day conversation also formal - so much about Italian informality: the formal plural is hardly ever being used nowadays, and would be Loro: scusino, signori, mi permettono di fare una domanda?), scusi/scusa is singular.

It's true that Italians don't always address each other using the formal way, but I think it's safer to assume as a visitor that one should always use it, at least at the beginning of a conversation. There are too many nuances to guess when it might be appropriate to use the informal, and there's a possible risk of offending someone (though most Italians I've met would be so pleased you are speaking Italian to them that they'd overlook it).

And by the way, permesso is also what you have to ask before entering somebody's home or office or whatever. Even if all greetings and handshakes have already been made outside, it would be impolite not to say "permesso" immediately before stepping across the doorsill (the host is going to answer "prego prego, s'accomodi"). It's literally the same word as "permit", and you can also use it in the extended version "chiedo permesso" - "I'm asking for the permit", literally.

There are a couple different ways to say that in most languages, sometimes it doesn't matter what you say, and others, one may just be more commonly used than others. For Romance languages, it's fairly obvious what the root of those words is and that it means about the same thing in English (scusi is from scusarse, the verb to excuse, permesso is from the verb permettere, to permit/allow). In English, you might say excuse me, pardon, sorry, etc. all for about the same thing. In some languages, you use the words or phrase for "please" in such a situation, also (por favor in Spanish, je vous en prie in French is used for excuse me sometimes, or I beg your pardon, as well as excusez-moi or just "pardon"). In Spanish, you could say perdone or "perdon!" or "con permiso", all of these languages have a lot in common. Sometimes you might more likely use one form if you are trying to get by someone, for example (con permis), and another if you did something you are sorry for (like stepping on someone's toe or burping). So in Italian, permesso would make more sense to try to get by someone.

What is the "oh please" remark for? I was asking about the difference.

The explanations are interesting, thanks.

Yes, enough with the "oh please" responses to civil questions! Those who can't reply without scorn should probably keep their remarks to themselves.

I had "scusi" and "scusa" exactly backwards, so I'm glad learn the distinction.

...but there was absolutely no harm meant. I should have written "attention, please", but in capital letters - I just thought this thread (not any particular posting) started to add more to confusion than to clarification.