public class MainFrame extends javax.swing.JFrame{
        private Competition comp = new Competition();
    public MainFrame instance = null;

    //we set the instance to current instance of MainFrame in constructor
    public MainFrame(){
        instance = this;
    }

    public Competition getCompetition(){
        return comp;
    }
}

public class AddSwimmerDialog extends javax.swing.JDialog {
        .....
        private void jButton1ActionPerformed(java.awt.event.ActionEvent evt) {
                //you create the object
                Swimmer s = new Swimmer();
                //now you need to store somewhere
                MainFrame.instance.getCompetition().swimmers.add(s);
        }
}