To create a Derby database first open the "Services" pane in NetBeans. Expand the "Database" node, then right click on the "Java DB" node and select "Create Database..." from the popup menu. This brings up a "Create Java DB Database" dialog.
NOTE: Do not expand the "Java DB" node. Due to a NetBeans idiosyncracy it interferes with creating a database.
In this dialog you need to fill in the 4 text fields. I recommend "app" for the user name. You can use any string with alphanumeric characters for the database name and password fields. The two passwords must be identical. Be sure to record the information that you enter into this dialog. You will need it later. When you are ready click the "OK" button.
After you have completed the previous step your database is created and a new node appears under the "Databases" node in the "Services"pane. Its icon indicates that it is not yet connected. That is your next step.
To connect to the database, right click on its node and select "Connect" from the popup menu. After you do this the icon for the database changes to indicate that it is connected. Then you can expand the node to see what's there.
Most of the nodes shown below are best left alone. The "APP" node is where you will be adding database tables.