A good place to start is our new white paper, The Java Language Environment.
http://java.sun.com/whitePaper/java-whitepaper-1.html
Next, if you haven't already done so, download a copy of the Java Developers Kit (JDK); see
http://java.sun.com/JDK-1.0/index.html
We strongly recommend that you do all your development work with the new (JDK) compiler and applet API rather than the older alpha 3 version. Note that Java-enabled browsers, such as Netscape, require beta or later (JDK) applets. (The alpha 3 HotJava browser, on the other hand, only understands alpha applets.)
Now you're ready to work through The Java Language Tutorial.
http://java.sun.com/tutorial/index.html
Note: This is an on-line draft version of The Java Language Tutorial by Mary Campione and Kathy Walrath. This is the fifth book in the The Java Book Series to be published by Addison-Wesley and is due out this summer.
After this, you'll know enough to follow your interests and dig deeper: class API's, the Java Language Specification, and so on, all of which you can find starting from our documentation page:
http://java.sun.com/doc.html
There's also a lot to learn from applets written by others, and many applet writers make their source code available on their web pages. See
http://java.sun.com/applets/
for pointers to applets that we and others have written. Note that some of the pages here have beta applets and others have alpha applets.
Finally, you can use the Java-related newsgroups (comp.lang.java and alt.www.hotjava) to ask questions and discuss Java programming.
Enjoy!