How can I add “posted by ‘author'” to each post?

A plug-in might use the_content filter to append / prepend this, but if you’re a theme author or otherwise are able to edit the the theme templates directly.

In this case you want to edit your theme’s single.php. (You can always check which template file is being used by a particular page using this answer: https://wordpress.stackexchange.com/a/10565/9364).

single.php is used for single posts, and other post types if they do not have their own template (you see how WordPress decides what template to use here).

In single.php you should find something like

 <?php get_template_part( 'content', get_post_format() ); ?>

Which includes another file depending on the post’s format. For a normal post, this will be content.php. (Please note this may vary by theme – the upshot is that you want to find where it calls the_content()) – the_content() is what displays the post content.

Below that you want to add something like:

the_author();

(see codex). Check the TwentyTwelve theme for more ‘involved’ example.