Your initial question is 'what does a QA person do'. A QA person is responsible for ensuring that the application, database, etc. being tested functions as stated and provides the functionality that is required by the organization. That being said, you can approach this by many different means. What I would do (as a former QA person) is look at what is being tested. Does your boss want you to test the application or database or both? Whatever it is, you need to be aware of how the vendor states it is supposed to function and what are your company's requirements are for this product. This will provide you with a list of what you want to test. From there, you need to determine how you will test to find out if it functions as is required. The lists given in the above replies is a good start for the database.
This is just a brief description. Any more questions, just post them and I'll try to answer.