Salta is a city in Argentina.
South towards Cafayate
Take bus #5 (without letters) from Av. San Martin, near Parque San Martin to village Cerrillos (6.30 pesos) or to El Carril (Chicoana) or even to Coronel Moldes, buses have additional notes on their windshield with their route, you need a transports' card "Saeta" or use somebody's card and give them cash. Get off the bus at the end of the village, find a good place for hitchhiking. There are a lots of local transport or full cars so be patient and use all capabilities to move forward.
North towards Jujuy
There are two main roads to go north. Ruta 34 (passing by General Guemes) has high transit and although longer (124 km) it will be probably faster. The other, Ruta 9, is more touristic. It runs through a beautiful scenery, but to cover the 90 km you have to relay on other tourists on car. To try out the latter route get the bus #6C to Vaqueros (10 pesos, as of 2018) or #6 to La Caldera (15 pesos).
Other useful info
To pay in the city- and suburban buses you need a transports' card "Saeta" or use somebody's card and give them cash.