(Remember, backup any files you edit code to!)
That’s also quite easy. To get rid of the date (and the author) in your loop.php theme file delete this code:
<div class="entry-meta">
<?php twentyten_posted_on(); ?>
</div><!-- .entry-meta -->
If you want to keep the author bit ‘by Chip Bennett’ etc. then you need to edit the function itself in the themes functions.php file and take out the date bit but leave the author.
As for the ‘Posted in’ bits edit the loop.php and delete the following code:
<?php if ( count( get_the_category() ) ) : ?>
<span class="cat-links">
<?php printf( __( '<span class="%1$s">Posted in</span> %2$s', 'twentyten' ), 'entry-utility-prep entry-utility-prep-cat-links', get_the_category_list( ', ' ) ); ?>
</span>
<span class="meta-sep">|</span>
<?php endif; ?>