Just use HTML in the JLabel text.

http://java.sun.com/docs/books/tutorial/uiswing/components/label.html

http://java.sun.com/docs/books/tutorial/uiswing/components/html.html

This will work in an Applet but I'm sure not in an application.  I
remember asking this question years ago but I don't remember the answer
I got.  It may have been better than this one :-).

import java.awt.*;
import java.awt.event.*;
import java.applet.*;
import java.lang.reflect.*;
import java.net.*;
import javax.swing.*;

public class test2 extends JApplet {
    public void init() {
        try {
            EventQueue.invokeAndWait(new Runnable() {
                public void run() {
                    JLabel l = new JLabel("Knute's Website");
                    l.addMouseListener(new MouseAdapter() {
                        public void mousePressed(MouseEvent me) {
                            AppletContext ac =
                             test2.this.getAppletContext();
                            try {
                                ac.showDocument(new URL(
                                 "http://www.knutejohnson.com"));
                            } catch (MalformedURLException murle) {
                                murle.printStackTrace();
                            }
                        }
                    });
                    add(l);
                }
            });
        } catch (InvocationTargetException ite) {
            ite.printStackTrace();
        } catch (InterruptedException ie) {
            ie.printStackTrace();
        }
    }
}

...

It is a common question with no simple, straight forward answer.

What sort of information are you opening in the link?
Is it from the your site?  Do you have control over it?

This is easy enough with regular label with a MouseListener
attached, the mouseEntered event can be used to show the link
as 'active'.

That makes it tricky.  None of the methods of opening a browser
from an *application* include the option to specify 'target'.

OK, you ready?

Applet can use the showDocument method, but browsers never
had to implement it, there is no report of success or failure, and
many pop-up killers interfere with it.  It  does allow to specify a
target, which can be ignored by the browser if it chooses.

I would avoid it, if the information in the links is anything more
than trivial.

Applications.

Pre 1.6 applications would have to rely on BrowserLauncher2
(3rd party APIs), while 1.6+ can use the Desktop.browse()
functionality.  Desktop reports success/failure, AFAIR, BL2
throws exceptions if it cannot find(/launch) the browser.

JWS (J2SE 1.2+) applications or applets have access to
BasicService.showDocument()..
<http://www.physci.org/jws/#bs>

Ultimately, it is easiest in a JWS app.