Actually, it's confusing but Java and Javascript are two different things. If you disable Java, it will prevent Java "Applets" from functioning in web pages. A good example of a Java applet is the little interactive graph that comes up when you look at stock charts on smartmoney.com. Javascript, on the other hand, is used for things like making menus drop-down automatically on websites (there are other ways to do this, too, and there are MANY other uses for javascript, but it's a common example).
To disable Javascript in Internet Explorer, go to Tools > Internet Options > Security > Custom Level. Near the bottom of that list, you'll see a "Scripting" section. Generally, if you're disabling javascript, you just want to disable "Active Scripting". The "paste operations" function is handy for autocompleting forms and stuff and I don't think it's a great security risk, so I wouldn't think you'd need to disable that part.
You can find information on disabling javascript in other browsers and more information here:
http://javascript.about.com/library/bldisable1.htm
edited to say:
By the way, I wouldn't really recommend disabling the Java JRE that Aric mentioned, but perhaps there are reasons to do so. For that matter, I don't think javascript is THAT huge of a deal either if you keep up to date on your software patches (updates) and use basic security measures (firewall, virusscan, etc.).