One good way to get started is to look at Sun's Java Tutorial. Here are some excerpts and examples:

• Object Oriented Programming
• The canonical "Hello World" applet
  • Demo Applet -- prints Hello World in a little box in your browser window...
• Life Cycle of an Applet
  • Demo Applet -- note the changes in the box if you iconify and reopen your browser window while on that page
• Events and User Interfaces
  • Demo Applet -- note the changes in the box if you move your mouse into and out of the box