To do what you want, you need to download and install the Oracle Java web plugin from java.com.
Before doing that, please see below.
Java on the Web (not to be confused with JavaScript, to which it's not related, despite the similarity of the names) is a weak point in the security of any system. Java is, among other things, a platform for running complex applications in a web page, on the client. That was always a bad idea, and Java's developers have proven themselves incapable of implementing it without also creating a portal for malware to enter. Past Java exploits are the closest thing there has ever been to a Windows-style virus affecting OS X. Merely loading a page with malicious Java content could be harmful.
Fortunately, client-side Java on the Web is obsolete and mostly extinct. Only a few outmoded sites still use it. Try to hasten the process of extinction by avoiding those sites, if you have a choice. Forget about playing games or other non-essential uses of Java.
Java is not included in OS X 10.7 and later. Discrete Java installers are distributed by Apple and by Oracle (the developer of Java.) Don't use either one unless you need it. Most people don't. If Java is installed,
disable it —
not JavaScript — in your browsers.
Regardless of version, experience has shown that Java on the Web can't be trusted. If you must use a Java applet for a task on a specific site,
enable Java only for that site in Safari.
Never enable Java for a public website that carries third-party advertising. Use it only on well-known, login-protected, secure websites without ads. In Safari 6 or later, you'll see a lock icon in the address bar with the abbreviation "https" when visiting a secure site.