Problem:
How do I digitally sign my java applet?

Solution:
You need to get a signature ID from one of the various companies that
distribute them.  What this gives you is a private key and a public
key.  You sign your applets with the private key and give out your
public key so that everyone else can decrypt your private key.  
Attached is a URL for one such company:

http://verisign.netscape.com

brief steps for signing a java applet:
1) you develop applet
2) get signature ID from above URL
3) use private key to sign your applet
4) clients get your public key and enter it in their database
5) run applet