Things I wish I had known before my first visit to Pompeii:
In general the Rick Steve's guidebooks provide good directions for independent travelers; I have not duplicated his directions here, but I have added some clarifications and details.
The usual way to reach Pompeii is by train from Naples. Note that there are two different train lines: the National Italian railway (with service from Naples to Rome and other major cities) and the local Circumvesuviana railway. These two rail lines depart from the same central station in Naples (Garibaldi), but on different levels. Make sure the train you get on in Naples is destined for Sorrento; not all of the branches of the Circumvesuviana stop at Pompeii. The Circumvesuviana goes south from the central station in Naples; several of the most interesting sites (Herculaneum, the villa at Oplontis, and Pompeii) are a short walk from Circuvesuviana Stations. The Circumvesuviana train stops directly at the Pompeii excavation site; the stop is called Pompeii Scavi, and this is the main entrance to the excavation through the Marina gate.
The Villa Laura is a pleasant hotel in Pompeii; the rooms are large with marble floors (some have terraces), and the charming breakfast room serves wonderful cafe latte and hot rolls. (If you plan to stay at Villa Laura, note that it is much closer to the National Italian railroad station in the contemporary city of Pompei than to the Circumvesuviana station at the Pompeii Scavi excavation entrance.)
I prefer to stay in Sorrento at the lovely Albergo Loreley et Londres, Sorrento:
Loreley & Londres Via Califano 2, Sorrento, Italy, Phone: 081.8073187 . (Rick Steves describes this hotel in his guide book.) Don't expect four star accommodations: the place is a little run down and the plumbing is temperamental. However, the view of the Bay of Naples from the dining terrace is spectacular (on an unusually clear day, you can see Vesuvius), the staff are cordial, the food is wonderful, and the prices are very reasonable - and the place has a wonderful old world atmosphere. (Ask for a quiet room overlooking the sea; some of the rooms that face the street are noisy). Reservations can be made on line at: http://www.guestinitaly.com/hotels/sorrento/04.htm

You will need at least one full day to see the Pompeii excavation -- more time if you want to explore fully. It can be extremely hot in summer: a sunshade/umbrella and bottled water are helpful. There is a cafeteria within the site. The line of guidebooks produced by Bonechi are beautifully illustrated and available in just about any language one might want.
At the Torre Annunziata stop (about halfway between Pompeii and Naples) you can visit the Oplontis villa that is said to have belonged to Poppea. Your Pompeii ticket will get you free admission to the Oplontis villa on the same day. When you get off the train, walk out the front door of the station, turn left, and walk one block until you reach a main street; at that point, turn right and walk downhill about five long blocks (at the turn, you will begin to see signs that direct you to the villa).
Herculaneum is also accessible from the Circuvesuviana: get off at the Ercolano stop and walk downhill toward the sea about 8 blocks. Note that there is no refreshment stand and only chemical toilets available once you get inside the site; come prepared.
Most of the art and artifacts from Pompeii have been placed in museums. The Museo Nazionale Archeologico Napoli has the most extensive collection; it is well worth a visit. Rick Steves gives clear walking directions to the museum from the subway station.
In Sicily there are numerous Greek and Roman sites that are well worth seeing, including Agrigento, Solunto, Segesta, and Syracusa. My favorite site is the Roman villa at Piazza Armerina with its spectacular mosaics showing hunt scenes (and the famous "bikini girls"). It is in a remote mountain location that is impossible to reach by public transportation, and might be difficult to find if you are driving yourself around. If you want a terrific driver and guide to take you to the great archeological sites in Sicily, I highly recommend Lorenzo's taxi service in Palermo. Lorenzo is punctual, pleasant, and a very safe driver! His web site is worth a visit even if you aren't planning to visit Sicily.
A few travel web sites feature my novel as recommended background reading for people who plan to visit Pompeii, and I wish to return the favor by listing their sites (I have not actually booked tours through any of these organizations).
Here they are: