Yes, Italy is a parliamentary democracy, similar to the UK. The president has mostly a protocolar job and the government is voted in by the parliament.
Now, AFAIK (because I might be mistaken, I’m a long wy from being familiar with the Italian electoral system) :
For a long time, Italy didn’t have a “first past the post” (I believe it’s the correct english name) system. As a result, Italy had a large number of parties represented in the parliament, and the governments were formed by coalitions of parties (like in Israel) that were necessary to form a majority, which resulted in very unstable governments (alliances could change in-between elections, a particular issue could divide the parties making up the government, etc…). A dozen years ago or so, this was replaced, if I’m not mistaken, by a first past the post system, but Italy still had more parties of significant importance represented in the parliament than in the UK, hence still used coalition government (for instance Berlusconi has been allied with the “Northern League” that wants to split up from southern Italy, and with a party that was formerly neo-fascist).
I explained this because Italy has a reputation of extreme political unstability that doesn’t really apply anymore.
Right before the elections, Berlusconi changed the electoral law, and if I understand correctly, for the first time, people voted for a list presented by each party at the national level (instead of electing a MP in each circonscription). The list with the most vote will get at least half the seats, and the rest of the seats will be attributed proportionnally to the votes, which is a rather unusual electoral system. Officially it has been devised to ensure a stable majority, but Berlusconi’s party didn’t really hide that they expected it to be more advantageous for him for some reason (maybe the left is more divided and he expected that the largest leftist party was less likely to have more votes than his own. Only a wild guess). The senate will be elected in the same way, except that it will be regional lists instead of national lists Also, the senate has mostly the same powers as the lower chamber, contrarily to what generally happens in unitarian (as opposed to federal) democracies. I suspect this is intended to satisfy Berlusconi’s allies from the Northern League.
As for the voting method, they use paper ballots. From what I watched on TV, electors are handed a rather large sheet of paper divided in small squares with a symbol and party name on each. They seem then to put a rather small ballot in the ballot box. So, I suspect (but it’s a wild guess) that the small squares are actually stickers, that the voter picks one and stick it on some paper ballot.