learn the Italian language with Italian culture

If you have found work and are coming to live in Italy, you’d better get used to being a straniero (foreigner)!
Italians split stranieri into two groups: comunitari (those coming from member states of the EU) and extra-comunitari.

First of all you will need un posto da vivere (somewhere to live). The most logical solution is to affittare un appartamento (rent a flat). For this you can check local agenzie immobiliari (estate agents/realtors) or look in numerous free newspapers left in street stands.
Once found, you will need to fare il contratto (draw up and sign a contract) and agree on the affitto (rent). When budgeting you will need to think about other expenses too - le bollette (utility bills), and le spese condominiali (joint expenses for the upkeep of the apartment builiding).

Whilst on the subject of money, you will need to aprire un conto corrente (open a current account) at the local banca (bank) or ufficio postale (post office). A word of warning - bank accounts are seldom gratis (free) in Italy, hunt around for the best offer.
Once opened, you can have your stipendio (salary) paid into your account - either by setting up a bonifico (standing order) or paying in an assegno (cheque).

Now for the hard part! Italy is notoriously full of redtape. Mettersi in regola (getting ‘legal’) can involve traipsing around public offices for days on end to compilare moduli (fill in forms) and fare i documenti (organise documents).
Basic documents include the codice fiscale (a kind of national insurance code) which can be obtained at the local ufficio delle entrate (’income’ office) and is needed for practically everything from getting a job to buying a mobile phone. Do this first!
Next you should investigate what kind of permesso (permit) you need to stay/work in Italy if here for longer than three months. Comunitari can immediately apply for residenza (right to residence) at the local comune (town hall). Having residenza also means cheaper bollette! You might also want to consider getting a carta d’identità (id card), also done at the comune, as you are legally required to carry with you some form of identity.
After 5 years you are also entitled to apply for cittadinanzà (citizenship).
Another important document is the tessera sanitaria (medical card) which gives you the right to free(ish) medical care. Apply for this at the local ULSS (National health service) office. Without this you will be in for a long wait at pronto soccorso (casualty / ER) in the event of being taken ill!
So, buona fortuna (good luck) and pazienzà (patience)!