How do I apply for the residence permit within 8 days?

Short answer: Within eight working days of entering Italy, send the postal kit to the Questura of your city, through a post office or your university's permit desk (MUR circular). It costs €116.46 for a permit of up to one year: €16 stamp, €70.46 card fee, €30 postal fee (University of Pisa).

1. Buy the €16 marca da bollo at a tobacconist.
2. Get the free kit at a post office with a "Sportello Amico".
3. Fill in Modulo 1 in black pen and capitals, with the stamp on page one. In the visa reason field, follow your university's guide; Genoa's PhD guide shows a worked example (University of Genoa PhD guide).
4. Enclose copies, not originals: passport pages with data, visa and entry stamp; enrolment or pre enrolment certificate; scholarship letter; health insurance; accommodation proof; codice fiscale if you have it.
5. Pay at the counter and keep the receipt (user ID and password) and the Questura appointment letter.