As other friends have previously mentioned you can create a Panel,add all the buttons in the panel and finally add scrollbar to the panel.
here is my simple code that does the job:
import java.awt.BorderLayout;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JPanel;
import javax.swing.JScrollPane;
public class ArrayOfButtons extends JFrame{
    final static int numberOfButtons=5;   
    // Label to display the message indicating which button generated the event.
    JLabel label=new JLabel();
    // Panel to accomodate the labels
    JPanel panel=new JPanel(); 
    //We create an array of buttons whose number depends on our choice  
    JButton buttons[]=new JButton[numberOfButtons]; 
public ArrayOfButtons(){
    super("Demo");
    //We create an instance of the class ButtonHandler which implements the interface
    //ActionListener. And this object "handler" is basically the object that handles 
    //the events.            
    ButtonHandler handler=new ButtonHandler();  
    //Using a for loop we create JButtons.    
    for(int i=0;i<numberOfButtons;i++){
        buttons[i]=new JButton("Button"+i);
        // here we register handler as the event listener for all the buttons.i.e if in 
        // case an event occurs in any of the buttons, the event listener (in our case
        //the handler object) calls an appropriate method that handles the event.            
        buttons[i].addActionListener(handler);
        // add each button to the panel
        panel.add(buttons[i]);
    }
   // we add the label to the JFrame 
   add(label,BorderLayout.SOUTH);
   // we add ScrollPane to the JFrame and in turn add Panel to the ScrollPane.
   add(new JScrollPane(panel));      
}
// This is an inner class that handles the events.(Look more on inner classes).
 public class ButtonHandler implements ActionListener{   
    //This method is called in case an action event occurs.For example you click on the
    //button      
     public void actionPerformed(ActionEvent event){
         // gets the name of the button and displays in the label.
         label.setText(event.getActionCommand());
     }       
}
}
Add a main method of your own, and the code will work just fine. Hope this will help.