Syria is the only country which currently has an open land border with
Lebanon - the border with Israel is likely to stay closed for some time. Neither
Syria nor Lebanon will issue visas for the other, so make sure you get your
visas before you leave home. Buses run between Beirut and Damascus several times
a day, and there are also buses and service taxis from Beirut to Aleppo and Homs,
or from Tripoli to Lattakia and Homs. If you're planning to drive into Lebanon,
be prepared to pay a hefty fee at the border - it's refundable when you leave,
but it can be very steep.
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 and 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.