There are a lot of interesting Italian phrases that can help you connect with other Italians and better make sense of their culture. If you want to talk with someone in Italian or frequent locations in Italy then it will be incredibly constructive to be familiar with common terms and sayings. This is valuable if you plan to stay at any small villages or deal with rural locals. It will go a long way in gaining their confidence if they can speak their own common language and comprehend you clearly. Making an effort in this department will pay off both in the short and long term if you have a prolonged stay.
One compelling Italian saying refers to the degree in which you fail can choose the outcome. Just because you do fail does not mean it has to be the end of all things. This phrase would be, "Non affoga colui che cade in acqua - ma affoga chi male incappa". This loosely translates to "Who falls in water doesn't drown - but who falls badly will". Another phrase or saying is one you are probably very familiar with. It is without doubt a classic. Here it is: "A caval donato non si guarda in bocca". This fundamentally means, "Do not look a gift horse in the mouth". In other words, just be delightedou get anything at all instead of worrying how nice it is. Sage advice to be sure. You may or may not have the convenience to use these in usual conversation, nevertheless hey you never know. It could happen. I predicate your conversation partner would be impressed.
How about a few more? Here's an entertaining one: "Chi dorme non piglia pesci". As with the preceding one, you have most likely heard this one several times. It fundamentally means, "The early bird catches the worm". I presume this is good advice in any culture. You can find this particular phrase in plenty of languages all over the planet. This is a quaint one: "La gatta frettolosa ha fatto i gattini ciechi". This means, "The rushed cat will make blind kittens". This one is positively odd, but I would have to admit that you do not want to rush a pregnant feline. No good fortune can come of that I am willing to wager.
The right way to be taught Italian phrases is to dwell amongst Italians. No astonishment there, though it is the sure fire course of picking up the nuances of any language. This goes for all languages, of course. If you truly want to comprehend it then you must be around the people who grew up with it. This is your reason to take a vacation.