I did this by implementing an Othello playing engine in Java, then loaded that applet into a web page and called methods in it using JavaScript embedded in the page. This worked pretty well; all browsers of that time eagerly supported Java applets without complaint. Because Internet Explorer was the foremost browser at the time, I also used a Microsoft ActiveX control to display an animated "genie" (similar to the infamous "Clippy" paperclip in Office), which did speech synthesis and recognition.
Times have changed, and today ActiveX controls are all but dead and Java applets are no longer acceptable for implementing client-side logic. With modern browsers not even including Java by default, my Othello page sat broken and neglected under the tide of progress.
After eight years of ignoring the problem, I finally decided to rework my Othello game implementation. The new version uses only Javascript (no Java applets), and should work in all modern browsers (I've tested it in Firefox, IE, Opera, and Safari). In the interest of standards compliance, the page also validates as XHTML 1.0 Strict.
Othello Game
Let me know if you have any trouble using this in your browser!