First of all, I am not – by any means – a PHP or WP whiz. I tinkered around with the NGG template files/code until I found a solution that works for me. I hope this at least might get you close to what you are trying to achieve.
My Solution:
Step 1. Open the Singlepic.php template file:
nextgen-gallery > views > singlepic.php
Step 2. Rename the singlepic.php file to something else like singlepic-caption.php
(The hyphen caption seems to be the right way to rename the template files. You might find another way to name the files, but this seems to work well for me.)
Step 3. Add the following PHP call to the code after line 21 of the above file (or really, wherever you want the text to be displayed):
<?php echo $image->alttext; ?>
or
<?php echo $image->description; ?>
***NOTE*** I found the alttext version seems to display a little better on my server for some reason. Give both a shot to see which works better for you.
At this point you should be able to style as needed.
Step 4. Upload the renamed/edited file to your server.
Step 5. In a WP post or page, use a new singlepic shortcode including the name of your new template like this:
[singlepic id=1 template=caption]
This solution seemed to work for me. I hope it works for you – Good luck!
***UPDATE*** Just thought of this: If you are using Float in your single pic shortcode, you may need to style the above call with matching right or left floats in the template/style and then create seperate templates to correspond to your singlepic shortcode float. Again, good luck!