Database testing is an type of testing where we test the database data in order to check the whatever the operations we perform in fronted are available in data base properly. In other words to check the impact of fronted operations on backend database in terms of data validation and data integrity.
Ensure that application should display proper alert message on form feed and in process, Once the Database server is down. Exception Handling Mechnaism should be application for this.
Testing is the verification of the customer requirments and black box testing are test that only knows the input and the output of the test, but not knowing the internal mechanism of the test.
This is a big area with a lot of methods and esp. if you want if from the basics.. The best thing is to attend a course or read a book about it. I recommend "Foundations of Software Testing" by Dorothy Graham.