Since Lebanon is a small country, getting around is very easy and not a problem. Planes and trains are not available for local transport. Several people choose to walk. Other options include buses and cars or taxis.
Lebanon has a good connection of buses. They will connect you to different cities very well and fairly quickly. Bus travel is also cheaper. There aren't any proper schedules as such, with buses departing as and when they're full. If you want to cover a short distance, go by service taxi. They can be hired in advance and can carry 4 or 6 passengers. You can also rent a car, but, car rent is very expensive here.