Communication

By air

Hazrat Shahjalal International Airport is well served by international flights from most continents. Biman Bangladesh Airlines is the national carrier of Bangladesh; which is well connected in 18 international destination. Mainly in Middle East also Malaysia, Singapore, Thailand and also Indian Subcontinent.
Indian Airlines, Jet Air has direct flights from Kolkata / Delhi/ Mumbai. Pakistan International Airlines has direct flights from Pakistan. Thai Airways also has direct flights from Bangkok There are also gateways from Nepal on GMG Airlines and Bangladesh Biman, Hong Kong on Dragon Air, Malaysia, Singapore, Delhi, Kunming and Kolkata. You can also travel to Dhaka from Middle East by Gulf Air, Emirates, Qatar Airways, Etihad Airways, Kuwait Airways, Saudi Arabian Airlines, Yemenia, and Both Dhaka & Chittagong by Bahrain Air, Turkish Airlines, Oman Air and Air Arabia.

Shahjalal airport is modern and reasonably efficient. However, half the world's mosquitoes seem to live in the baggage reclaim area, so be sure to wear long sleeves and covered legs/feet. Also note that immigration takes a lot of time during peak hours (minimum 30-45 mins) as the system is manual and there are only 2 lines for foreign passport holders.

By bus

Being the capital and geographical center of the country, Dhaka is the natural hub for the country's bus companies. There are several bus stations around Dhaka, and which one you need to be at depends where you want to go, so ask around before heading out to one of them. Most are as crowded as you would expect them to be(because of population).
Sayedabad bus station is useful for buses to the eastern half of the country including Sylhet Division and Chittagong Division.
Gabtali bus station serves most of the western half of the country including Jessore, Rajshahi Division and Khulna Division.

Mohakhali bus stationserves mainly to Tangail, Mymonsing and other northern districts of Dhaka. Sometimes also Bagura and other western-northern part of Bangladesh.
Luxury buses like Green Line, Shyamoli, Silk Line,Saudia-S alam (Mercedes bench) and Shohagh serve the major cities and tourist attractions. They all have a few offices around town, the most central being those near the Eastern Hotel on Inner Circular Rd in Central Dhaka, just north of the Motijheel area. Green Line serves Chittagong (400 taka, 5-6 hours), Cox's Bazar (630 taka, 8-9 hours), Rajshahi ( Tk 350, 4 hours), Sylhet (Tk 400, 5 hours), Khulna (Tk 450, 7 hours) and Jessore ( Tk 400, 5-6 hours) in its comfortable Volvo buses. It also has a couple of super luxury Scania buses to Chittagong (Tk 550) and Cox's Bazar (Tk 850) if you feel comfortable floating through a developing country in high style and have enough taka to spend(however the money spent could go towards helping develop Bangladesh more). Seats are huge and fully recline. The quality of these buses are comparable to Business class of an airline!! (there are also Hino A/C luxury buses as well as Volvo and Scania). Recently, the S.Alam and the Saudia, two of the leading (non-ac) bus service providers have jointly launched a Mercedes-Benz luxury bus service to Chittagong, Cox's Bazar and some other major cities. One of the ticket counters has been opened at the Panthapath, an area where you can locate all major luxury bus ticket counters.
From India there are a number of land entry points for Buses. The most common way is the regular comfortable a/c buses from Kolkata to Dhaka via the Haridaspur / Benapole border post. Private bus companies Shohagh, Green Line, Shyamoli and others operate daily bus services. Government buses run under the label of the state owned West Bengal Surface Transport Service Corporation (WBSTSC) and the Bangladesh Road Transport Corporation (BRTC). WBSTSC and BRTC both operate buses from Kolkata every Tuesday, Thursday, and Saturday at 5:30AM and 8:30AM, and 12:30PM while from Dhaka they leave on Monday, Wednesday, and Friday at 7:00AM and 7:30AM. The normal journey time is around 12 hours with a one-way fare of Indian Rs.550 or Tk.600-800, (roughly $8-12). If you're only headed to Haridaspur the fare is Rs.86, or Tk 116. The journey should take around 2.30 hours.

By boat

Most ferries arrive at and leave from Sadarghat in Old Dhaka. This area and the streets surrounding it are unbelievably hectic so allow plenty of time and watch your bags and pockets carefully. If arriving here, fight your way to the left on the frontage road and then make your first right - this turns into Nawabpur Road and leads north to the hotels. Even if you aren't staying in this area, it's easier to walk several hundred meters north to catch an onward rickshaw, the ones near the ghat are at a standstill.
The Rocket Steamers (P.S. 'Tern', 'Masud' and 'Ostrich') run to Barisal and Khulna several times per week, departing from Sadarghat around 6pm. To Barisal is Tk 480/300 in first/second class, while all the way to Khulna will run Tk 1010/610 and take 26-30 hours. Tickets should be booked at the BIWTC office in Motijheel just east of Dilkusha Circle I. It's open until 5PM Su-W and until 2PM on Thursdays, closed on Fridays. A quick heads-up in that the link to the BIWTC tariff mentioned above is in 'Takas' and one should double check the fares.

Chandpur is the second major river station 3 to 4 hours journey from Dhaka and 5 to 6 hours Journey from Barisal.
Multiple other boats are available for short and long distances - head to Sadarghat or Badam Tole ghat (about 1 km further west) and ask around. Tickets aren't pre-sold, and bargaining is likely necessary.