Dhaka has no metro system, so transport means roads, which are usually jammed during daytime hours. For short distances, the ubiquitous rickshaws provide a comfortable, cheap and generally pretty swift means of conveyance. For longer distances, the locals use buses which are very cheap and by generally very crowded. Unless you speak Bengali, a preferred mode of transport is likely to be either a yellow taxi (A/C), black taxi (non A/C) or a green CNG (=small tuktuks). Taxis are more comfortable, through pricier, but since CNGs are smaller they are often faster if you have to negotiate traffic jams.
On some 'hartal' days in certain parts of the city (especially if an election is upcoming), motorized transport is liable to firebombing or other attacks, so for a stress free journey you may wish to either travel by rickshaw or just take a day off whatever travels you had planned. Travel is much riskier on some hartals than others; watching local television will give you some guide as to the severity of this, though local advice is invaluable.
Prices and facilities at hotels vary considerably. The most expensive hotels (Westin, Sheraton etc.) are more or less comparable to such hotels worldwide. If you have a tightly limited budget, you should nevertheless be able to find accommodation to suit it.
Seek advice from wherever you are staying on this. Unless you are feeling adventurous, you should probably avoid food which is sold by the roadside, though tea from teashops should be no problem. Bottled water is probably the simplest option if boiled water is unavailable where you are staying.