Well, you've got a couple of choices, but none of them involve a direct low cost airline flight from any of the three Berlin airports to Emilia-Romagna or Tuscany, because, to date, no such service exists.
In fact, the closest Italian city to Bologna or Siena which you can fly to from Berlin (on any of the German or Italian low cost airlines) is... Rome.
Air Berlin flies from Berlin Tegel to Rome Ciampino.
VolareWeb flies from Berlin Schoenefeld to Rome Fiumicino.
However, even once you get to Rome, you'll still be faced with travelling into the city centre from the airport and then taking a three and a half hour train to Siena or a two hour forty minute express train to Bologna. This might not be quite what you're looking for (and it will certainly add to the price).
You could try travelling from Berlin to a German airport which does have low cost flights to Bologna or Siena but your options are also quite limited in this respect.
germanwings flies directly to Bologna from Cologne Bonn airport... but that's quite a long journey from Berlin in the first place and probably the expense of taking the train from Berlin Zoo out to Cologne and then connecting to the airport would make the final cost of the journey quite expensive, even with a very cheap germanwings ticket.
A very outside alternative would be travelling from Berlin to Frankfurt Hahn and then taking a direct RyanAir flight to Bologna Forli... but getting to Frankfurt Hahn can be hellish even from Frankfurt, never mind Berlin.
So, having exhausted all the low cost airline alternatives for the time being, it only remains to look at what Alitalia and Lufthansa have to offer.
Alitalia has no direct flights from Berlin Tegel to Bologna. Your only option with the Italian carrier is to take a flight from Berlin Tegel to either Milan or to Prague Ruzyne and then take a connecting flight to Bologna. Needless to say this is very expensive (around 600 euros).
Likewise Lufthansa only has connecting flights via Munich and Frankfurt/Main airports which is no better.
A really imaginative final alternative - and one which might involve some long hours waiting around in an airport in order to economise on the cost of the flight - might be to find two connecting low cost flights.
You might try this option:
Germania Express from Berlin Tegel to Frankfurt/Main
Then travel overland from Frankfurt/Main to Frankfurt Hahn
Then, RyanAir from Frankfurt Hahn to Bologna Forli
This isn't really ideal, because the transport infrastructure between Frankfurt/Main airport and
Frankfurt Hahn airport (which is practically on the other side of Wiesbaden) is still not terribly good.
Or, you might try this option (on reflection, perhaps this is much more straightforward):
Hapag Lloyd Express from Berlin Tegel to Cologne Bonn
or germanwings from Berlin Schoenefeld to Cologne Bonn
and then...
germanwings from Cologne Bonn to Bologna
With a little bit of careful planning, you might be able to get both germanwings flights for
19 euros (including taxes and charges) since germanwings have just launched a special offer on all flights booked over Christmas and New Year (from December 22nd until January 4th).
Let me know how it goes.
You can also find links to the english pages of all the low cost airlines above on:
http://www.attitudetravel.com/germanlowcostairlines.html
