-The simple version.

1) In the current installation go to Tools -> Export, and export an XML copy of your WordPress Database.
2) In the current installation Download your wp-content folder.
3) In the cPanel use Simple Scripts to install WordPress. See: http://tutorials.bluehost.com/wordpress/
4) In the newly made installation go to Tools -> Import, and import your previously exported XML file. See: http://tutorials.bluehost.com/movewordpress/
5) Upload your previously backed-up/downloaded wp-content folder and overwrite the wp-content folder which was created by Simple Scripts in the installation.
6) Log into your dashboard for the new installation, select your theme, double-check your plugins, and re-save your Permalinks settings(even if they already seem to be set correctly).

-The detailed version.

A) Before getting started you should check a few things. As a pre-warning, do *not* cancel hosting at wherever your old installation may be until you have confirmed that the newly imported WordPress setup with BlueHost is working properly. You may need to go back and get more things from the previous location should you find you missed something.
B) Make sure your current installation is running the latest version of WordPress. If it is not, deactivate your plugins and then upgrade it, or at least make sure it is running a fairly new version and you can upgrade it from Simple Scripts later.

1) Log into your current WordPress dashboard and navigate to Tools, and then click Export and “Download Export File.”
2) Using FTP, connect to your current account and download your wp-content folder. This folder will contain all of your themes, plugins, images, videos, etc. (If you have images which you have manually referenced from another location besides in your wp-content, you may want to change their location and reference location to be somewhere in your wp-content/uploads directory)
3) In the BlueHost cPanel use Simple Scripts to install WordPress. Make sure to install the exact same version of WordPress you were running at the previous location. You can upgrade with Simple Scripts later, but for now, the two versions must match. See: http://tutorials.bluehost.com/wordpress/
4) In the newly made installation go to Tools, then to Import, and then to WordPress and search for and import your previously exported XML file. See: http://tutorials.bluehost.com/movewordpress/ (*Note that if you are importing a rather large file, you may need to increase your max_upload_filesize in your php.ini file. See: http://helpdesk.bluehost.com/index.php/kb/article/000110)
5) Using FTP, upload your previously backed-up/downloaded wp-content folder and overwrite the wp-content folder which was created by Simple Scripts in the installation. If you compressed your wp-content directory, you will need to uncompress it before uploading it. If you are not familiar with using FTP, download the FileZilla client from http://filezilla-project.org/ , then see: http://tutorials.bluehost.com/filezilla/
6) Log into your dashboard for the new installation, select your theme, double-check your plugins, and re-save your Permalinks settings(even if they already seem to be set correctly).

-Aftermath of the Migration
After finishing, you should click around on your site and make sure that things are working properly. If you are having problems, try deactivating some plugins. Another warning is to be careful on which plugins you choose. Always try to keep plugin-usage to a minimum and carefully choose plugins which have been tested and proven with more recent versions of WordPress.

If you were not already running the latest version of WordPress, deactivate your plugins, set your theme to the default theme and begin upgrading. Check your site between each upgrade and make sure that standard features are working properly. If you find a plugin breaks something after an upgrade, you may need to search for another plugin to replace the functionality of the plugin which was breaking things.

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(On a separate note, if you just changed your URL too, you will likely need to make some post-settings, or site-URL settings changes. For help with this, see: http://wordpress.shadowlantern.com/how-change-wordpress-url-phpmyadmin/

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