There are two types of taxis in Beirut; the old (often) battered hail-taxis, and the prebooking taxis.
Hail-taxi - The most convenient form of transport in Beirut, as they are absolutely everywhere. Those taxis are predominantly Mercedes Benz cars (though recently, due to increasing petrol prices, taxi drivers are opting for more economic forms or transport) and can be pretty easily identified by their yellow illuminated taxi sign on the roof and red number plate. Fixed meters aren't provided so it is recommended to ask how much your trip will cost before hopping in. The fare will be charged per destination and not per distance traveled (which is an advantage since traffic is a big problem in the city).
A typical journey from one side of Beirut to the other (roughly 3 km) may cost LL10.000 (€5.00). Many taxi drivers speak at least a few words of English and French. Knowing the name of your destination in the local language may solve any misunderstandings. note: keep in mind the names of the landmarks around the city, as they will come in handy when traveling by public transport (some drivers mightn't be that good at orienteering!).
Prebook taxi - These require that you call them and book a ride, they generally cost more but are much more luxurious and are normally air conditioned. All hotels should provide you with a taxi directory, if you wish to use this type of service. Taxi prices are considered cheap if compared to US and European taxis. Major taxi companies are: Geryes Taxi (00961-1-332747), Taxi Premiere (Tel 1260 or 00961-1-389222). Allo Taxi (Tel 1213 or 00961-1-366661).
The more common form of transport, especially with daily commuters, as they are cheaper than the taxis, but ironically, are in fact the same. Service [ser-vee-s] are shared-taxis, the same taxis as above but shared between four people. The biggest advantage with the Service system is that the price of the ride is fixed at 2,000 L.L (€1). They come with drawbacks of course, and apart from having to share a small car with three other complete strangers (great for meeting new people actually), Service drivers may choose not to take you if you are not going in the same direction as them. Hailing a service or taxi usually entails yelling your destination to the driver if he slows down, then chasing the name of your destination with either 'taxi' (for private taxi 10,000 L.L.) or 'service' (for service 2,000 L.L). It is important that you specify what type of ride you want (when hailing a taxi or service), if you fail to do so, the driver will assume you asked for taxi, and will overcharge you at taxi-rate. However if the driver stops to ask for other fares or picks up another passenger only pay the Service rate of 2,000 L.L.
There are currently two public transport companies. The OCFTC  that operates a fleet of blue and white city-buses, and the LCC  with a fleet of red and white minibuses; Bus fares cost around 600 to 750L.L ($0.40 to 0.50). The service is very efficient and the buses come very often, to get onto a bus you must stand at the side of the road and signal with your hand as a bus approaches; the buses will stop anywhere.
Driving in Beirut is not to be recommended for much of the day, particularly in the city center. Traffic is heavy, and impossible during rush hour. There is so much to see and being stuck in a traffic jam is the last thing anyone would want to spend their time doing. Walking around the city is much more of an experience, and is in fact necessary in the very center since that part of the city is a pedestrian area. It can be difficult to find parking other than in multi-story and off-street car parks. On-street parking, if you are lucky enough to find one, is allowed for a short time of two hours. Tickets must be purchased through the parking meters usually located at either end of a street. They can be paid by either cash or card. Overstaying your time may get you a ticket. Enforcement of the parking limit isn't done very efficiently, but obviously the last thing anyone would want to find is a ticket that will ruin their day and set them back financially. Renting a car is recommended if you're planing to visit neighboring towns and cities such as Jounieh, or if you're planing to go out late at night when public transport isn't operating, or maybe simply to enjoy the Lebanese "see-and-be-seen" lifestyle. Car rental prices range from economical 40.000L.L/day (€20.00/day) to luxury and exotic standard prices. Those can change according to season, so make sure you contact the car rental company beforehand to check prices as well as pickup/drop-off locations. Driving in Beirut is on the right-hand side of the road. Only the central areas of Beirut have traffic lights operating, though plans have been made to cover all of the city.
As the city is quite compact, walking is the best way of getting around, and perfect for getting off the beaten track to find unexpected surprises. Streets are generally well signposted, but few Beiruti locals would know how to navigate according to their names, directions are usually given by building placement ("straight down the road until you reach building X, turn left there, then right..."), and many streets have local nicknames that wouldn't match the map. That said, if you find yourself lost in the streets, simply ask any passer-by for directions; no one will refuse to help! Otherwise you can stop at the nearest hotel or shop and ask. Hotel concierges and shop keepers will most definitely speak English. Some roads in Beirut are in poor condition. Not so much in the center, but the farther you get from downtown the more road works you will most probably find. So take care! You can always check out a Beiruti-run walking tour called Walk Beirut. They offer weekly tours around the city.
A word of caution for pedestrians. Crossing roads which you have frequently to do, is very dangerous. Beiruti drivers do not give pedestrains precedence and although they won't run you over on purpose they won'r respect the few pedestrain crossings there are and traffic lights are also hazardous. In additon many streets are one way, but scooters and sometimes also cars ignore that, so watch out, look both sides several times and once you have spotted a gap, step out confidently and continue. Don't hesitate you you can be in danger.