The droppings will be small and black, often resembling coffee grounds or ground pepper. 

The more you can detect their droppings means there are more cockroaches present. Ewww

Cockroaches can produce a strong and disturbing odor. 

The smell of cockroaches is musty, oily or mildewy.

Female cockroaches lay their eggs in a casing called an oothecae. Female cockroaches can lay from 10 to 55 eggs at a time. 

Since cockroaches lay dozens of eggs, you can easily find this casing which is strong signs of an infestation. 

Seeing a cockroach in the home is a solid sign of an infestation. 

A combination of droppings, eggs and large numbers of cockroaches mean a nest is near and infestation occurring. 

Look for these signs near pipes or electrical wiring, under refrigerators and sinks and in old book cases and cabinets.