You need to understand that MVC doesn't directly reference .aspx pages like WebForms in its URLs. Its main purpose is to separate concerns, that is model (data), controller (logic), and view (presentation).

First, you'd have to create a route matching your URLs, which would now look like this for example : /home/search/This+is+my+search+string

This would call the Search action method of the Home controller, which would get "This is my search string" as an input parameter. This action is responsible for accessing the model and pulling the results probably from a database.

Typically, your search action would then return a ViewResult containing the view placed in the folder /Views/Home/Search.aspx. Here, you can use neither the Postback functionality nor the events of your Web controls like in WebForms, because MVC applications are stateless and not event-driven. It's more like a request/dispatch way of doing things.

Read more about MVC here.

You can use a simple javascript in the button's onclick to redirect to the search page:

Search <input type="text" id="go" size="4" /><input type="button" value="<%=Html.Encode(">>") %>" onclick="javascript:window.location='<%=Url.Action("Search", "Home") %>/' + document.getElementById('go').getAttribute('value')" />

Create a user control called Search.ascx with a form:

<% using (Html.BeginForm ("Search", "Home")) { %>
    <input name="search" type="text" size="16" id="search" />
    <input type="image" name="search-image" id="search-image" src="search.gif" />
<% } %>

And in your search action all you need is the following:

public class HomeController : Controller
{
    public ActionResult Search (string search)
    {
        throw new Exception (string.Format ("Search: {0}", search));
    }
}

In your master page or wherever you can then add

<% Html.RenderPartial ("Search"); %>