JFileChooser chooser = new JFileChooser();
if(chooser.showOpenDialog(frame) == JFileChooser.APPROVE_OPTION){
File file  = chooser.getSelectedFile();
FileReader reader = new FileReader(file);
}


This is just a minimal bit  of code, but it should do the job. There are
lot of other features that you can use as well, such as file filters,
but I will leave that up to you. You can also take a look at the Java
API documentation for the JFileChooser and see the example they provide.