How do I redirect a user when a button is clicked?

It depends on what you mean by button. If it is a link:

<%= Html.ActionLink("some text", "actionName", "controllerName") %>

For posting you could use a form:

<% using(Html.BeginForm("actionName", "controllerName")) { %>
    <input type="submit" value="Some text" />
<% } %>

And finally if you have a button:

<input type="button" value="Some text" onclick="window.location.href='<%= Url.Action("actionName", "controllerName") %>';" />

Just as an addition to the other answers, here is the razor engine syntax:

<input type="button" value="Some text" onclick="@("window.location.href='" + @Url.Action("actionName", "controllerName") + "'");" />

or

window.location.href = '@Url.Action("actionName", "controllerName")';

If, like me, you don't like to rely on JavaScript for links on buttons. You can also use a anchor and style it like your buttons using CSS.

<a href="/Controller/View" class="Button">Text</a>

if using JQuery, you can do this :

<script type="text/javascript">
    $('#buttonid').click(function () {
        document.location = '@Url.Action("ActionName","ControllerName")';
    });
</script>

It has been my experience that ASP MVC really does not like traditional use of button so much. Instead I use:

  <input type="button" class="addYourCSSClassHere" value="WordsOnButton" onclick="window.location= '@Url.Action( "ActionInControllerHere", "ControllerNameHere")'" />