In single.php (you see only one post here) the place is really under

<?php the_content('Read the rest of this entry &raquo;'); ?>

just write in the next free line "this is a test custom text"
and check any of your posts, it should show up.

What is the error you get?

Joern you are brilliant! Thanks to one of your other post on an unrelated topic I was able to answer my second question: How to add "Read the full story" to category excerpt?

Just in case there are other searching for the answer, here's the solution ==>
in archive.php look for <?php the_excerpt(); ?> then add the following code:

<a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>">Read the full story &raquo;</a>

How to add custom text at the end of each post?
I would like to add custom text at the end of each post, for example: copyright, signature, etc. According to WordPress the code should be added to single.php under

<?php the_content('Read the rest of this entry »'); ?>

however, when I add my html code there I get an error message. Can you tell me where to add this code?

How to add "Read the full story" to category excerpt?
Can anyone tell me where to add the code to "Read the full story" (see below) for the Category excerpts?

<?php the_excerpt(); ?>
" rel="bookmark" title="Permanent Link to <?php the_title(); ?>">Read the full story »

"Read the full story »" shows up on the home page but not when you browse by category.

Any help would be greatly appreciated.