Remove by Author and Category from Posts

What theme are you using?

override it in your functions.php child theme:

function twentytwelve_entry_meta() {

	$date = sprintf( '<a href="%1$s" title="%2$s" rel="bookmark"><time class="entry-date" datetime="%3$s">%4$s</time></a>',
		esc_url( get_permalink() ),
		esc_attr( get_the_time() ),
		esc_attr( get_the_date( 'c' ) ),
		esc_html( get_the_date() )
	);

	printf(
		$date
	);
}