Take for example, the New Products sidebox ...
The original files are located at:
You would copy those files to your templates and override directories, where your_template_dir is the directory for your templates and overrides:
NOTE: I always copy both peices of a sidebox even if I am only changing one peice so that there is no confusion in the future ...
In this case, to remove the price, you need to remove it from the:
file so that it does not display, and you will see a line that reads:
simply comment that out:
$content .= '<div>' . $whats_new_price . '</div>';
Now you will not see the price in the New Products sidebox ...
// $content .= '<div>' . $whats_new_price . '</div>';