UPSRTC runs city buses between the different archaeological sites in Agra. Taxis are another great option. You can hop onto a prepaid taxi from right outside the airport or the railway station. Prepaid autorickshaws are also available. Various tour operators ply buses, taxis for their customers.
If you feel like mingling with the local crowd, then ride your way through the city on a bicycle. Un-metered autorickshaws, tongas (horse driven carriage) are other options for tourists to explore the city. Agra being a tourist haven, local, unwitting customers often have to be careful when negotiating prices to ride on an un-metered autorickshaw, tonga, cycle rickshaws to get from one place to another.