There are three different modes of public transportation that you can use in Qatar: buses, taxis and limousines, all of which are owned by Mowasalat Karwa apart from some limousine companies.
The bus service began in October 2005. Ticket prices start from just Qr4.00. You can travel as far north as Al Shamal/Al Ruwais, as far west as Dukhan, and as far south as Mesaieed Umm Said. You will be requiring Karwa Smart Card to purchase ticket in Bus. No cash Handling in Bus since 2010.
An alternative to taxis and buses would be to use a limousine service, which will send a car to your location as will Karwa taxis if they are booked by telephone. Limousines are expensive, but they are the most comfortable form of transport.
You can hire a car with local Car Rent companies. You will find plenty car rent company in City, in Air port or Hotel.
Walking and using bicycles is usually not a good idea in the hotter months of the year, as the heat can get very intense and tiring.