public class MainFrame extends javax.swing.JFrame{
        public static Competition comp = new Competition();
}

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.comp.swimmers.add(s);
        }
}