Search results still showing old domain name
I have posted a few other posts here about changing my domain name, and as of right now everything is working. To back up a minute, I am hosting my own siite on my macbook using a DYNDns account. About a year ago I needed to change my domain name. With help from you fine people I was able to figure out how to do so, but I am still having a minor issue. What i did to change the domain name was to just open another DYNDns account for the new domain name and point it to the same IP address of the old domain name (the IP address of my macbook). So technically speaking both my olddomain.com and newdomain.com are pointed to the same IP address and displaying physically the same site. All SEO since the new domain was opened was done through the new domain address.
My problem is that when I search for my site through Google, it shows up with good results and displaying the correct name, title and description of the site, but it is listing the old domain address not the new one.
I am ready to let my old domain account expire and use solely my new domain, but if google is technically speaking loading th e site through my old domain address when clicking on a result, how do I change it so Google is displaying and loading the correct (new) domain address in its results?
I can assume the following, but heard it also may take a few weeks for google to update so I need a definite answer first... If I were to use an .htaccess file using a 301 redirect for my old domain to my new one, google "should" eventually update. Am I correct on this assumption? Using this technique brings up a novice question. Since both domains are pointed to physically the same site, a user wouldn't get into an infinite loop constantly trying to redirect them would they?
What are anyone's thoughts on this and how to tell google to display my new domain in its results and not my old one?