Dismantle the bed and stand the components on end. Things to look for are the bugs themselves and the light-brown, molted skins of the nymphs. Dark spots of dried bed bug excrement are often present along mattress seams or wherever the bugs have resided. Oftentimes, the gauze fabric underlying the box spring must be removed to gain access for inspection and possible treatment. Cracks and crevices of bed frames should be examined, especially if the frame is wood (bed bugs have an affinity for wood and fabric more so than metal or plastic).
Successful treatment of mattresses and box springs is difficult and infested components may need to be discarded.
Alternatively, place a bed bug proof mattress cover over an infested mattress to trap the bed bugs inside and starve them to death. This will eliminate the need to purchase a new mattress/boxspring and make treatment and future inspections easier. (Starving the bugs CAN take up to 400 days, so make sure your cover stays sealed for at least that long.) 
Bed bugs also hide among items stored underneath beds.
Empty nightstands and dressers. Examine them inside and out, then tip them over to inspect the woodwork underneath. Oftentimes, the bugs will be hiding in cracks, corners and recesses.
Check upholstered chairs and sofas. Pay close attention to the seams, tufts, skirts and crevices beneath cushions. Sofas can be major bed bug hotspots when used for sleeping.
Check other common places. These include along and under the edge of wall-to-wall carpeting (especially behind beds and furniture), cracks in wood molding and ceiling-wall junctures. Bed bugs tend to congregate in certain areas, but it is common to find an individual or some eggs scattered here and there.
Use a flashlight. Inspectors sometimes also inject a pyrethrum-based “flushing agent” into crevices to help reveal where bugs may be hiding.