how to handle the Click button event in MVC

ASP.NET MVC does not work the same as ASP.NET WebForms. Or rather, I should say ASP.NET WebForms does not work the same as the rest of the web(!).

When you create an HTML form is has an action attribute that specifies the URL that should handle the form submission. When the user submits the form, through an input or button with type="submit", the browser does a POST request to that URL, including the data contained in the form through using the application/x-www-form-urlencoded MIME type by default (different if the form should include file upload).

Your server-side code should not be responding to individual UI events as this is not how the web works, WebForms merely gave you an abstraction over HTTP to lure you into a sense of control that does not exist on the web.

Here is two example action methods that would handle the GET and POST requests for the form:

public ActionResult Index()
{
    var model = new MyFormFields();
    return View(model);
}

[HttpPost]
public ActionResult Index(MyFormFields fields)
{
    if (!ModelState.IsValid)
    {
        return View(fields);
    }

    // do stuff with form data

    var model = new MyResultModel
    {
         Output = fields.Input // for e.g.
    };

    return View("Results", model);
}

This responds to the form submission and renders a different view with the results view model. Best practice suggests doing an HTTP redirect here such that the browser can't resubmit the POST request by accident, but we'll leave that for later.