Public transportation is, without question, a very economical way to navigate and get around Cusco. Not only is public transportation relatively cheap, it's also a wonderful way to learn about different areas of the city and to experience Cusco from a local's perspective.
Aside from public transportation, many locals walk from one place to the another. The city is very walkable and abounds with tourists, however, always make sure to walk in groups when going to the Plaza de Armas (main square) or to other areas of the city. Also, it's important to note that most roads are made of cobblestone and it's recommended that you pay attention to where you walk due to uneven surfaces.
Bus/Minibus - For public transportation, buses and minibuses have a fixed route throughout the city. The cost per ride is very economical. Keep in mind that Cusco is not a large city and that most roads are very narrow and are made of cobblestone. While some students do use the bus/minibus system, this is may not be the preferred means of transportation.
Taxis - Here is another extremely inexpensive mode of public transportation! When using taxis make sure to agree on the tariff before getting into the vehicle, as there are no meters, and that way you are not overcharged. All taxis within the main part of Cusco have a fixed rate of 2-4 soles (meaning 65 cents to a little over a dollar). They should not overcharge you. However, they may charge extra if going to an outer part of the city, or if they have to enter the airport, as they are charged for entry. If you are going to the airport, ask them to drop you off outside the airport if you would like to avoid the additional cost.