This route begins at the far end of the Torre del Greco Wharf (Molo di Torre del Greco), winds through the town of Torre del Greco, and hops on the Via Vesuvio road all the way up to the entrance of Vesuvius National Park. Up to that point, the road is paved. At the National Park entrance (~14k and ~1000 m elevation) the paved road turns to dirt and brings you the rest of the way to the first look at the crater. Once you spot the crater, continue on the permitted path along the crater rim (due south). Pass several vendors until the very last vendor along the crater rim (south end of the crater). To continue would mean either going out of bounds, or going down a descending trail. This is the turnaround point. Use the same route to return to the Torre del Greco wharf. Enjoy the wild ride back down.
A few more notes: Secure your entry ticket to the National Park before beginning the route. Cost is around 10 Euros (in 2023) and can be purchased online on the official national park site. Options for buying food/drinks along the middle section of the route are limited in winter, but abundant in higher seasons of tourism. Note that it is not permitted to circumnavigate the entire crater rim, including reaching the highest point of the crater. Be safe and observe posted signs. Thank you to Thomas Summer for inspiring the Vesuvius ascent.
IMPORTANT NOTE - FORBIDDEN TRAIL
You can find an alternative route here called "Forbidden route". In February 2023 the FKT team realised that the route created in 2018 and the consequent FKT by Thomas Summer was invalid, because it crossed a prohibited area next to the summit. That variation route is left here in the notes for archive purposes but cannot be chosen for further FKT attempts. In case of doubts, please look carefully at the sign at the beginning of the forbidden trail (see photo enclosed here).
For sake of memory Thomas did that route in 2h31m.
Please read the comments about the forbidden route and DON'T TAKE IT.