The public bus system in Hanoi is extensive and extremely cheap—only VND 5000 per ride, just over one American quarter. However, some of the routes are maddeningly circuitous, turning short trips into long excursions. Riding at peak hours is not recommended, both because the coaches are flat-out packed and because they move with excruciating slowness through the gridlock. In general, expats find other forms of transportation to be more efficient and less stressful than public buses. When you ride the bus, be especially wary of pickpockets.
Buses run from early morning (5 a.m.) till about 9 p.m. A conductor collects fares in cash, and will have change for small bills, but anything above VND 20,000 may be a problem. Most city maps indicate bus routes, and some of the major routes are listed on the internet here: http://www.firstchoicevietnam.com/content/Transportation+in+Vietnam/16/1119.