Once my employer's nulla osta is approved, how long do I have and what are the next steps to actually enter Italy?

Approval of the nulla osta is a milestone, not the finish line. You take the authorisation to the Italian consulate or embassy in your country of residence and apply for the long-stay work visa, submitting your passport, the nulla osta, and supporting documents.

After you arrive in Italy, you must complete the residence steps quickly: typically you sign the contract of stay (contratto di soggiorno) at the immigration desk (Sportello Unico) and apply for your residence permit (permesso di soggiorno) within the first days of entry. Keep to these deadlines, because the permit is what makes your stay and work lawful beyond the visa's initial entry.