Alexandria is quite a long city; you can get pretty much anywhere by using the local transportation available along the Corniche.
By taxi
Alexandria's yellow and black taxis are a good way to travel in the city, and a cheap one as well. Be careful though: taxis will uniformly refuse to use meters the rates haven't been adjusted in years and drivers love to take advantage of non-Alexandrians, so it's best to agree on the fare before you get in. No taxi ride between any two points in the city should cost more than 25LE. Alternately, if you are on a day trip to Alexandria, hire a taxi outside the railway station for the day and pay LE 10-15 per place. E.g., if you plan to see 5 places in 3-4 hours, pay around LE 50-60 to the driver or LE 80-100 if you plan to see 8-10 places in 5-6 hours.
To get into a taxi, wave at the driver and yell the name of your destination. If the driver agrees they would park at the side of the road as soon as possible. Some taxis will stop to pick you up even if they already have a passenger, but such offers are best refused. Futhermore, always check back once you get out of the taxi, there is no number to call if you lose anything of value, and nearly no chances of having it returned.
Fast Call taxis can be booked by phone at 19559 or 0800-999-9999 toll free. These are pricier but generally much better than ordinary black and and bright yellow cabs.
By Tram
Alexandria has a creaky, slow but very cheap tram system that dates back to 1860 and looks the part — it's the oldest one still running in Africa. The route map is remarkably confusing and changes on a regular basis, but one factor stays constant: the network is split into the interurban Ramleh Lines Tram el-Raml, which use blue-and-cream trams and run across the city a few blocks back from the sea towards the eastern suburbs, and the City Lines Tram el-Madina, which use bright yellow trams and run west and south of central Alex. The two meet at Raml Station Ù Øطة اÙر٠٠Mahattat el-Raml, right at the heart of Alex. For both lines, the flat fare is a whopping 25 piasters ~US$0.05, and tickets can be bought on board. Note that the first car out of three in the blue trams is reserved for women only.
Probably the most useful service for tourists is yellow tram #25, which runs from Raml Station to Ras el-Tin and Fort Qait Bey. You can also hop on any blue tram west from Sidr Gabr bus/railway station to get to Raml, but not all eastbound trams stop there.
By bus
There are a variety of local bus services which have improved significantly in the past few years, but they are rather confusing for those who haven't lived in Alexandria for a while. Apart from city buses, you will also find "mini-buses", which work on hop-and-go basis. They are easily recognizable 14-person buses, which will stop when you wave and stop where you need to get off. The drivers rarely speak English, so make sure you know the Arabic name of your destination or that you already know where to stop. The routes are usually along the main streets and cost between LE 0.50-1.50.