Changing servers and new URL, how to update database info?

I have changed servers and I’m going to have my WP installations on another domain name. How do I go about making sure everything is set to go? Here is the info I get when I go to desireebaker.com/memories:
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Error establishing a database connection

This either means that the username and password information in your wp-config.php file is incorrect or we can’t contact the database server at localhost. This could mean your host’s database server is down.

* Are you sure you have the correct username and password?
* Are you sure that you have typed the correct hostname?
* Are you sure that the database server is running?

If you’re unsure what these terms mean you should probably contact your host. If you still need help you can always visit the WordPress Support Forums.
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Thought I go straight to the horse’s mouth so I can get this done quickly.

TIA!