Hi there. Are you using the default WordPress theme?
Depending on how the by-line has been implemented in your particular theme, you may need to style ".entry-meta".
Just as @WPyogi suggested, always setup a child theme before making any changes.
The WordPress codex has a comprehensive article about child themes. Please digest it first, before making any changes to your theme files: http://codex.wordpress.org/Child_Themes
For instance, in twentythirteen, you can hide the by-line by adding this CSS style:
If you are running WP version 3.6, you can use the "Custom CSS" option in the Appearance section of your Admin Area to make this edit. Saves you having to edit theme files.
Hope this helps.