You will receive an email message at the address you specified in the form. In that message, there will be a snippet of HTML code. Cut and paste that HTML code to the page on your website where you told the ring system you were going to place them (on the form you filled out). A good place is either on the bottom of your home page or on your "links" page. Some webmasters even have dedicated "web ring" pages for the tags of all the web rings they belong to. This will allow your visitors to jump to other web sites in the ring easily. A webring isn't a webring without them!
If your web site is hosted on Homestead, you can find some good instructions on how to insert raw HTML code onto your web pages here.
If your web site is hosted on The Express Page, contact the ringmaster for a special set of HTML tags. You can disregard the first set of tags that are sent to you automatically when you apply.