This tutorial will give you two simple examples on how to host web-applications in CompleteFTP.
Before getting started, you need to enable the 'Server-side Javascript (JSS)' property, on the site which is serving up the page.
OR select the 'Sites' panel (Enterprise MFT).

Note that the owner of the /Public folder is the user called 'anonymous', which is hidden by default.
To show it, check the 'Show system users/folder/sites' item in the View menu at the bottom left.

Now, let's create our own web-application in Javascript.
In this example, we create a web-app that simply displays 'Hello world' and is available publicly.
response.write("Hello world");

In this example, we're going to create a .jss file in a user's home directory, and execute it as a JSS web application. This web-app will be available only to the user.
response.write("<h1>" + system.user.homeFolder + "</h1>");
response.write("");
var homeFolder = system.getFile(system.user.homeFolder)
var files = homeFolder.getFiles();
files.forEach(function(file) {
response.write("- " + file.name + "
")
});
response.write("
");

For more information on developing the JSS web-app, please refer to JSS Web-App Basics and the JSS API Guide.