I want to direct an easy to remember domain url to my website that has nothing to do with the brand or the original domain. What is the proper way to add a second domain to a website without opening up the chance for being penalized by search engines? I don't want the second domain to show up in SERPs.
Just do a 301 redirct from the short domain to the main domain. That will allow users to always find the main site and tell search engines the short URL doesn't really exist and to only index the main URL.