What’s the correct way to redirect visiting browsers and bots from a page that is permanently gone to a replacement page?

For permanent redirects opt for301 Redirect as that not only redirects the page but it also passes on the ranking elements/authority  from the existing page to the new location.

SEO wise (according to Google Webmaster Guidelines)301 permanent redirects are the best option. It makes more sense to follow up better webmaster practices and Google thionks this s the best regardless of any argument might be presented. 

301 Redirect

301 redirect is the most efficient and Search Engine Friendly method for webpage redirection. It's not that hard to implement and it should preserve your search engine rankings for that particular page. If you have to change file names or move pages around, it's the safest option. The code "301" is interpreted as "moved permanently".

You can Test your redirection with Search Engine Friendly Redirect Checker

Below are a Couple of methods to implement URL Redirection via code and htaccess redirect

IIS Redirect

In internet services manager, right click on the file or folder you wish to redirect

Select the radio titled "a redirection to a URL".

Enter the redirection page

Check "The exact url entered above" and the "A permanent redirection for this resource"

Click on 'Apply'

ColdFusion Redirect

<.cfheader statuscode="301" statustext="Moved permanently">

<.cfheader name="Location" value="http://www.new-url.com"> 

PHP Redirect

<?

Header( "HTTP/1.1301 Moved Permanently" ); 

Header( "Location: http://www.new-url.com" ); 

?> 

ASP Redirect

<%@ Language=VBScript %>

<%

Response.Status="301 Moved Permanently"

Response.AddHeader "Location","http://www.new-url.com/"

%> 

ASP .NET Redirect

<script runat="server">

private void Page_Load(object sender, System.EventArgs e)

{

Response.Status = "301 Moved Permanently";

Response.AddHeader("Location","http://www.new-url.com");

}

</script> 

JSP (Java) Redirect

<%

response.setStatus(301);

response.setHeader( "Location", "http://www.new-url.com/" );

response.setHeader( "Connection", "close" );

%> 

CGI PERL Redirect

$q = new CGI;

print $q->redirect("http://www.new-url.com/"); 

Ruby on Rails Redirect

def old_action

headers["Status"] = "301 Moved Permanently"

redirect_to "http://www.new-url.com/"

end 

Redirect Old domain to New domain using htaccess redirect

Create a .htaccess file with the below code, it will ensure that all your directories and pages of your old domain will get correctly redirected to your new domain.

The .htaccess file needs to be placed in the root directory of your old website (i.e the same directory where your index file is placed)

Options +FollowSymLinks

RewriteEngine on

RewriteRule (.*) http://www.newdomain.com/$1 [R=301,L]

Please REPLACE www.newdomain.com in the above code with your actual domain name.

In addition to the redirect I would suggest that you contact every backlinking site to modify their backlink to point to your new website.

Note* This .htaccess method of redirection works ONLY on Linux servers having the Apache Mod-Rewrite moduled enabled.

Redirect to www using htaccess redirect

Create a .htaccess file with the below code, it will ensure that all requests coming in to domain.com will get redirected to www.domain.com 

The .htaccess file needs to be placed in the root directory of your old website (i.e the same directory where your index file is placed)

Options +FollowSymlinks

RewriteEngine on

rewritecond %{http_host} ^domain.com [nc]

rewriterule ^(.*)$ http://www.domain.com/$1 [r=301,nc]

Please REPLACE domain.com and www.newdomain.com with your actual domain name.

Note* This .htaccess method of redirection works ONLY on Linux servers having the Apache Mod-Rewrite moduled enabled.