Easiest way to find out what Java you have on your PC is to enter "java -version" from a command prompt or shell. If you get a sensible reply, you probably have the JDK loaded correctly. If it says something like "java is not recognised as a file or executable program" then you might as well download the whole JDK. It is most likely that what you already have is the runtime environment on its own (JRE) which is of no use for developing software. Be sure whatever you download has "SE" (standard edition) somewhere in its name and you might as well get the most recent version, Java 6 also called jdk1.6.0. Follow the installation instructions to the letter, especially the bit about setting the PATH permanently.
And don't believe them about NotePad. Dreadful program. Ask your teachers about what to use as a text editor. I like JCreatorLE which can be used as a text editor.