I would start by setting up a regular HTTP server, like lighttp or Apache httpd.
You say you already have a command line program that does the actual work - As a first step, I would reuse that, and configure the web server to call your program using CGI - see forexample http://httpd.apache.org/docs/2.2/howto/cgi.html for apache
Finally, I'd pick some javascript framework like jQuery or YUI with Ajax capabilities to do requests to the server to call the CGI script from within a webpage. You could also create a form-based web application without ajax or any framework, but that would require you to stuff all kinds of logic in your program to generate HTML pages. By using Ajax, you can leave the command line application as is, and parse any responses it gives with javascript, and then use that to dynamically change the webpage in a way that would make sense to the user.
If this all works, then I would try to figure out how to package all these components. Perhaps you just want to create a simple archive with all the programs inside, or maybe you want to go as far as actually embedding the webserver in your program. Alternatively, you may want to do it the other way around and rewrite your program as an ISAPI module that you can plug into your webserver. Or if that's not integrated enough still you could write your own (partial) HTTP server. That's really up to you (I'd probably spend time and energy on searching for the leanest, meanest existing open source http serverr and use that instead)
At any rate, the prior steps won't be lost work. Most likely, developing the web page is going form a substantial part of the work, so I would probably create a quick and dirty working solution first using the age-old CGI trick, and then develop the webpage to my satisfaction. At that point you can already have an acceptable distributable solution by simply putting all programs in a single archive (of course you would have to tweak the webserver's configuration too, like changing the default port so it won't interfere with existing webservers.) Only after that I would spend time on creating a more integrated fancy solution.