As and EU citizen, you can stay in Italy (or in any other UE states) up to 3 months without any formality.
For stay more than 3 months, you will need one of these reason:
- a work (employed or self-employed)
- attending a recognized school
- sufficient resources (about 6000 euro for Italy if you are alone) and a private health insurance
- a EU citizen family member with one of the previous reason
To be self-employed, the easy way is getting a "Partita Iva" from the Revenue (Agenzia delle Entrate). It's free to get, but then you will need to keep a number of documents and compile several periodical declaration. I strongly suggest you to speak with an accountant (commercialista), because failing to comply with the bureaucracy can cost you a lot of money.
Keep in mind that, depending of the fiscal regime you will use (talk to your commercialista), you may need to pay some taxes and mandatory pension contribution even if you are earning nothing at all.
You could try to come in Italy and start your business in the first 3 months, so you can get the permission to stay more. After 5 years, you will the right of permanent residency.
The hard part will be finding clients for your business, I wish you the best but in Italy there still a lot of discrimination due to sex, age, religion, race, etc ant the economical situation is still declining.