WordPress has a complex template hierarchy that determines which template files are shown based on each page request.
Template files are called from the active theme's directory at /wp-content/themes/theme-name. For example, if you request a single post, the single.php file in the active theme's directory will be displayed. If you request an author, the author.php template will be displayed.
If WordPress can't find those templates, it looks for the next related template available, eventually falling back on index.php if it can't find specific templates, as detailed in the hierarchy and shown in this diagram (click for large version):
If you are trying to customise the author or post templates, it is best to do that by editing the author.php and single.php templates in your theme directory, rather than attempting to restructure the hierarchy (defined in wp-includes/theme.php) yourself.
If you are trying to create 'pretty urls', you can do that using the Permalinks panel under the Settings header in the WordPress admin area.