By air: Chittagong's Shah Amanat International Airport (CGP) has flights from Dhaka (about 45 minutes), the Gulf states (Doha, Dubai, Sharjah, Muscat) and a handful of regional destinations. Internal flights from Dhaka are the easiest way to arrive if you are short on time.
By rail: Chattogram Railway Station is one of the busiest in Bangladesh. The overnight trains from Dhaka (notably the Subarna Express and the Mahanagar Express) take 6-7 hours and have AC sleeper berths. Daytime trains are slower.
By road: The Dhaka-Chittagong Highway is the country's busiest road link. Long-distance buses leave every few minutes from both ends and take 6-8 hours depending on traffic. Several private companies — Green Line, Hanif Enterprise, Shyamoli — offer comfortable AC coaches.
By sea: The MV Bay Cruise occasionally runs from Dhaka to Chittagong; check current operations. International passenger ferries no longer use Chittagong.