Tea is the most common drink in Libya. Green tea and "red" tea are served almost everywhere from small cups, usually sweetened. Mint is sometimes mixed in with the tea, especially after meals.
Coffee is traditionally served Turkish style: strong, from small cups, no cream. Most coffee shops in the larger cities have espresso machines that will make espresso, cappuccino, and such. Quality varies, so ask locals for the best one around.
Alcohol is officially banned in Libya, though in reality, alcohol is readily available through a local black market anything from whiskey to beer to wine. It should be noted that penalties for unlawful purchase can be quite stiff. Travellers should always exercise appropriate common sense with respect to local laws, local sensitivities and traditions.