Buses travel between Beirut and other major towns, but service is infrequent and un-timetabled. There are plans to restore the country's inter-city bus service, but those plans are still on the drawing board. It's far less likely that the country's rail service will ever be restored. Car rentals are fairly expensive in Lebanon but if you shop around you can find surprisingly reasonable prices. The country is notorious for the bad condition of its roads and the hair-raising style of its drivers.
Road rules are effectively non-existent, traffic jams are ubiquitous and there are no speed limits.
On the up-side, in theory everybody has agreed to drive on the right, and fuel is cheap and easy to get. We encourage you to verify any critical information with the relevant authorities before you travel. This includes information on visa requirements, health and safety, customs, and transportation.