Nagarjunakonda is most easily visited as a day trip from Hyderabad, about 150 km away. By car or bus the journey takes around 3 hours each way. Buses run from Hyderabad's Mahatma Gandhi Bus Station (MGBS) to Nagarjuna Sagar town, from where auto-rickshaws and taxis connect to the dam jetty.
The boat to the island runs twice daily (typically at 9am and 1pm, returning at 12pm and 5pm, but confirm locally as timings change). The crossing takes about 30 minutes each way. Given the boat schedule, the 9am departure is strongly recommended — this allows time to see both the museum and ruins before the midday return. Coming back on the afternoon boat means a very late return to Hyderabad. Basic accommodation exists in Nagarjuna Sagar town if you prefer to stay overnight.