I would start with a flash or java applet wrapper. You can communicate with your application over a tcp connection and display the results in the flash or applet.
CGI is what you want; it will let you embed any program you want into a website, it was made for that purpose. Then perhaps embedding a few more options with PHP and HTML will let the user acutally input data into the program via the web. It should not be too hard.
Take a look here for more info: http://www.cs.tut.fi/~jkorpela/perl/cgi.html
I think that is a good pointer in the right direction. I hope that helps.
Here's a good intro to writing CGIs in C: http://www.cs.tut.fi/~jkorpela/forms/cgic.html
However, since you're a beginner, I'd recommend porting your program to PHP. It's a very easy language to pick up, and it's a much easier route than writing a CGI in C.
I assume the C program needs input while it's running and not via command-line arguments? If I'm wrong, you can just use PHP and shell_exec() to run the program. The function returns anything printed to stdout.
Such a page might look like:
$sim = shell_exec("/path/to/binary -a 5 -b 6");
echo $sim;
Where the string passed to shell_exec is exactly what you'd type on the command line.
I would recommend going with sockets. If your C program could set up and listen on a local or internet socket, you could use the socket facilities in any language to send it arguments and get output.
If that's going to be too much of a pain, have php exec the program while directing the output to some file. Then, have php read that file.
Looking at the output of your program, I think trying to print the results of shell_exec() will result in clobbered output.
So, you could shell_exec("/bin/program -arguments > /tmp/prog-tmp.txt") , then read prog-tmp.txt.
If you want a dynamic simulation, where the cars moves while you watch , you'll need an applet or flash.
A cgi program renders the page on each http GET/POST (on reload, submit etc) and that is probably not what you want.