The question is a bit broad but here a few salient points from the website:
You must be ready to take up employment for at least 20 hours per week (there are in particular limits if you have kids and no way to care for them should you find work, in that case you might not be able to get both Kinderbetreuungsgeld and unemployment benefits), possibly need to show up at some specific location or otherwise show you are actively looking for work.
The amount you receive is made of three distinct parts and the calculations are somewhat complex. If I understand all that correctly, you should get between 55% and 60% of your earlier net income, possibly more if you qualify for a family benefit and did not earn much (i.e. you can receive up to 80% of your previous income if the amount would otherwise be under EUR 857,73). There is also a small incentive/payment to cover extra costs if you participate in a training program.
You should get at least 20 weeks of benefits, possibly more if you worked at least 156 weeks in the last five years, if you are older than 40 or if you participate in a training program.
In principle, transferring benefits between EU countries is possible but I am not sure how well it works in practice and what you need to do for that. It might be easiest for you to contact the relevant agency in Italy and ask what they require as I think you would need to go through them in any case.
AFAIK, all these conditions also apply to Austrian citizens and your being Italian does not make any difference.