So you have bought an expired domain relevant to your web site, that is carrying some existing traffic, that is not be utilized, so you want to re-direct the traffic to your site. Well this is how you do it. There are various ways to do this, but I am going to touch on the most useful ways.
If you know anything about SEO, then you are probably familiar with the 301 redirect, although if you do not know much about coding, you might not know exactly what it is. There are two ways to do a 301 redirect:
You can access or create a .htaccess file, you upload it to your root folder, and is the first file that talks to the server when the web site loads. You can tell the server to redirect this domain to another domain. So this means whenever anyone types in the expired domain, it will redirect to your domain. This would also include any URL, e.g. expireddomian.com/exampleurl.htm, would also redirect.
In addition to that, you also set individual URLs to redirect to specific URLs. So if you checked the old site, from the expired domain, you might want to redirect some of the old pages, to the pages most relevant to your site.
Here is the code to add to your .htaccess file
You could also upload a file, like index.php, and contain a script that simply redirects the page to where you like. This also counts as a 301 redirect, and may be a lot easier for some of you to do, rather than stressing about messing around with the .htaccess file (which can cause major issues if you screw it up).
So if you had a page like expireddomain.com/exampleurl, you would create a new folder called /exampleurl/, and upload an index.php file into that folder.
Here is the line of code you need, you need to make sure you have apache server with php installed (which you most likely do):
301 redirects are generally best to use as they will like pass on other things like Google rankings and link juice.