Become a babysitter

Your profile says you are from Italy, so I assume here you are EU citizen. As such, you are free to live and work anywhere in the EU, including Berlin.
Most babysitting engagements are informal "cash-in-hand" type jobs, which is fine as a side income. The requirements differ from family to family, pay is negotiated individually and usually low.
If you want a more long-term commitment or work above a certain (low) number of hours, you should either find a babysitting agency that employs you (uncommon) or officially become freelancer (which involves quite a bit of formalities for registration, tax and social security liabilities, paperwork (keeping proper accounts) and training - read about how to become "Tagesmutter" to see which kind of certification is needed.