In a very simple terms Software testing methodology is nothing but a roadmap for the testing project. At the beginning of the project the PM, test PM, client and all other important projects members must sit together and decide how the testing will be done such as what STLC model will be followed, what would be the deliverables, schedule etc. Then test strategy document is used to detail out the actual implementation of the agreed methodology.
The concepts of black box and white box are test design concepts
A test designed from a black box perspective implicity ignores implementation details; yet is still testing the code.
A test designed from a white box perspective explicitly analyzes the implementation to help the tester derive a test. The execution of that test can be performed using a mock or stub, or may be executed through the user interface.
I agree with SQT007. Test methodologies describe a standard for implementing testing into your project/organization. They cover topics ranging from test analysis to test execution and test management. Some well known methodologies are: