Assuming you have access to your theme's files, there are two places you're going to have to look:
- index.php. This is responsible for displaying a list of blog posts on the front page of your site.
- single.php. This is responsible for displaying a single blog post.
Unfortunately, both of these files are likely to pull in a bunch of other files, depending on what is being displayed.
Taking the standard "Twenty Eleven" theme as an example, in index.php it uses the function get_template_part()to load whichever template file has been used in the post.
That means that it loads content.php, for posts using the standard template, content-gallery.php for posts using the gallery template, and so on ...
So, to change the way that the date is displayed on the front page of a site using this theme, you would have to alter all of these template files accordingly.
Inside the files, the date is displayed thus: <?php twentyeleven_posted_on(); ?>. I'm sure it'll be something similar or equally obvious in your theme.
Single.php is less work. It just pulls in the file content-single.php.
You would alter this in the same way.
I hope that is understandable.