Component testing is described fully in BS-7925 and should be aware that component testing is also known as unit testing, module testing or Program Testing. The definition from BS7925 is simply the testing of individual software components.
Component testing has often traditionally been carried out by the programmer. This has proved to be less effective than if someone else designs and funs the tests for the component. "Buddy" testing, where two developers test each other's work is more independent and often more effective. However, the component test strategy should describe what level of independence is applicable to a particular component.
Usually white box (structural) testing techniques are used to design test cases for component tests but some black box tests can be effective as well.