My Geek9pmBlog  is on a server shared with other domains, and I want to move the whole word press thing to a new server.  I now have a high speed internet, so it will not take long to download it. It is under 100 MB.

I have never tried to restore a Word Press install to another  site. Will it work? Can it be done? And suggestions?
You basically have to download all the files and export the DB as a SQL FILE. Then upload the files to the new server, and run the SQL file in PHPMyAdmin (for example) to create the new database. Then open the wp-config.php file and update the database details and paths.Tools->Export in the dashboard.

quote from that page:

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When you click the button below WordPress will create an XML file for you to save to your computer.

This format, which we call WordPress eXtended RSS or WXR, will CONTAIN your posts, PAGES, COMMENTS, custom fields, CATEGORIES, and tags.

Once you’ve saved the download file, you can use the Import function in another WordPress installation to import the content from this site.