The Italian per favore isn't used anywhere near as much as 'please' in English. Being British I was bought up to use please and thank you all the time, but my usage of the word 'please' would seem excessive here. In informal speech it can be dropped completely, yet the request retains the same politeness that would be in the English translation. Over the years I've grown to prefer volevo when making a request, the imperfect conjunction of the verb volere; which means to want, to desire or to wish. It wasn't what I was taught at university, but something I picked up when I was studying in Urbino, specifically one day in the bus station when I wanted to buy a ticket to go to a town nearby. Back then I copied the language I heard around me a lot, and in shops or in similar situations I'd use phrases I'd heard people before me use. The other way this verb could be used when making a request is in the conditional form, which is 'vorrei' in the first person singular, it can be translated as 'I would like'. So, if you wanted a piece of pizza you could use Vorrei/volevo un pezzo di pizza. If you tacked 'per favore' onto that it would seem excessive and too formal. The politeness of the phrase seems to come across in the conjugation of the verb.
In more formal settings there are other phrases you can use for 'please'. For example there's per cortesia or cortesemente, the latter of these can be translated as 'kindly'. There's also per piacere which also translates as 'please'. What you'll also see a lot of is the verb 'pregare', in both formal and informal language. It translates as to ask, to beg or to request. It is used a lot in the passive voice where rules or laws are concerned, 'si prega, 'one asks'. For example Si prega di non fumare, means 'Please do not smoke'. In informal language it's used more to convey the idea of begging, Ti prego di non dire niente. "Please don't say anything."
It's quite a complicated idea to convey, and seeing as the Milanese aren't exactly seen as being very warm people, I know others will have different experiences. It's a different way of structuring language, and I don't think I've still managed to crack it after all this time!