This is a HUGE area. You might want to start by familiarizing yourself with the testing methodology. A good place to start would be MIL-STD-810F, Method 514.5 (available on-line) that explains some of the basic concepts for testing of payloads on fixed wing aircraft. You should also pay particular attention to Appendix B, which describes some basic engineering information on vibration testing in general.
In order to do this task, you will probably need to perform a finite element analysis of the article in order to calculate the vibration modes and its response to dynamic (or quasi-static) loading. After you have optimized the dynamic response and have built the hardware, you will probably need to verify the modes (prior to a vibration test) through an experimental modal analysis. After you have correlated the modes with the analytical model and are satisfied that nothing will break during testing, you could hand-off the article to a test lab that will perform the actual qualification test.
pj
