Okay.
One thing: the Open/Save File Dialog Box will just return the path
where you will save or open your file.
So, you have to do the two things (get the file path and save/open it)
in two times.
I thing code explain better than my (really) bad English:

[START OF CODE]
import java.io.File; //We need that to use the File object
import javax.swing.JFileChooser; //It show open and save dialogs

public class IO {

   public void saveFile(){
       String path = ""; //Variable who will contain the path where
we will write our file
       JFileChooser fileChooser = new JFileChooser(); //Object that
we will use to select our file

       int returnValue; //Variable who whill contain the value of the
ShowSaveDialog function (if user click "save" or "abord")
       returnValue = fileChooser.showSaveDialog(null); //Show a "save
window"

       if (returnValue == JFileChooser.APPROVE_OPTION){ //If user
click "save"
           File file; //We create a new File object
           file = fileChooser.getSelectedFile(); //We open the file
           //Normally, here you write into your file
           System.out.println("We open the file: " + file.getName());
       }
       else{ //The user click "abord"
           System.out.println("The user don't want to save the
file!");
       }
   }

   public void openFile(){
       String path = ""; //Variable who will contain the path where
is the file that we will read
       JFileChooser fileChooser = new JFileChooser(); //Object that
we will use to select our file

       int returnValue; //Variable who whill contain the value of the
ShowOpenDialog function (if user click "open" or "abord")
       returnValue = fileChooser.showOpenDialog(null); //Show a "open
window"

       if (returnValue == JFileChooser.APPROVE_OPTION){ //If user
click "open"
           File file; //We create a new File object
           file = fileChooser.getSelectedFile(); //We open the file
           //Normally, here you read from your file
           System.out.println("We open the file: " + file.getName());
       }
       else{ //The user click "abord"
           System.out.println("The user don't want to read the
file!");
       }
   }

}
[END OF CODE]

Don't forget to read the doc'!
How to use File Choosers: http://java.sun.com/docs/books/tutorial/uiswing/components/filechooser.html
(note that my example is here)
How to read/write from files: http://java.sun.com/docs/books/tutorial/essential/io/charstreams.html

Good luck.
Regards.