A service is a shared taxi, and costs 1000LL per person (service drivers will sometimes ask for more if the distance is far). Ask the service driver to go to the Khalifeh Restaurant, Shatila, near the Sabre Hmadeh intersection. From the Khalifeh Restaurant follow the directions on the map, or call the CYC to arrange for someone to meet you there: 03 974 672.
Make sure you ask for a service; taxis will charge you more. Vans also run between the Airport and Downtown, along the Tariq al Matar (Airport Road), and know the Khalifeh Restaurant well. Vans charge 500LL per person.