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As That Guy has already said - ideally you want to setup 301 permanent redirects.
More on 301 redirects at;
http://support.ecenica.com/domain-names/301-redirects/
If your website is hosted on a Linux server, you can edit your .htaccess either by hand, or if your web hosting company includes a control panel, like cPanel - you'll be able to edit it via your browser.
If you're hosted on a Windows server you can setup redirect using IIS or again, though your control panel.
We also recommend setting up a Google Webmaster account and telling Google that you're moving the domain.
http://support.ecenica.com/web-hosting/search-engines/what-is-google-webmaster-tools/
It normally takes a few weeks for site traffic to return to normal levels after changing the domain.
Also take a look at the canonical meta tag to prevent duplicate content showing in case both domains are listed;
http://support.ecenica.com/web-hosting/search-engines/how-to-stop-duplicate-content-in-google-yahoo-bing-and-ask-com/
Hope you find some of the above useful.
^RM.