In a JFrame, use a small WindowAdapter to listen to the WindowOpened event. From there, simply request the focus for the JTextField.

 import java.awt.*;
import java.awt.event.*;
import javax.swing.*;

public class MyFrame extends JFrame {

   JTextField field1;
   JTextField field2;
   JPanel panel;

   public MyFrame() {

  super( "This is my Frame" );

  panel = new JPanel();

  field1 = new JTextField( 10 );
  field2 = new JTextField( 10 );

  panel.add( new JLabel("Field 1:"));
  panel.add( field1 );
  panel.add( new JLabel("Field 2:"));
  panel.add( field2 );

  getContentPane().add( "Center", panel );
  
  addWindowListener( 
    new WindowAdapter() {
      public void windowOpened( WindowEvent e ){
          field1.requestFocus();
      }
    }
  ); 

  pack();
  setVisible( true );
   }
}

To try it:
import java.awt.*; 
import java.awt.event.*;
import javax.swing.*;

public class MyFrameApplet extends JApplet {

  public void init() {
     MyFrame myFrame = new MyFrame();
  }

}