There are many train options from Cairo (Ramses Station) to Alexandria and it's usually not necessary to book in advance. The best is the Express train which takes about 2-3 hours (depending on the stops).  The TurboTrain is no longer operating since December 2007 because it was too expensive. A first class ticket costs around US$7 one way.

You can also get a train from Alexandria to El Alamein and Mersa Matruh (handy for those wanting to visit Siwa Oasis).

Alexandria has two train stations, and the first one you may stop at (if traveling from Cairo) is Mahattat Sidi Gaber which serves the eastern suburbs of the city. As a tourist you'll probably want to get off at the second train station in Alexandria called Mahattat Misr (Misr Station) which is about a mile south of the city center. A quick taxi ride away from most of the centrally located hotels or a tram ride away from most of the sights.