Some themes display author bylines and author profiles and some do not. http://wpbtips.wordpress.com/2009/08/15/author-displayed-or-not/ There is no free way to move, remove or hide the byline other than switching to a theme that does not provide one.
If you do not wish to chnage themes then you will need to purchase an annually renewable Custom Design upgrade and do the required CSS editing.
http://en.support.wordpress.com/custom-design/
Important note: CSS editing is theme dependent. In some authors, themes, categories and/or tags etc. cannot be hidden independently, as they are in the same selector as the other meta data elements such as date, and perhaps even the “leave a comment” link, which means if you hide one, then you hide them all.
http://en.support.wordpress.com/custom-design/editing-css/