The core trick to generate different css classes for posts in the first coliumn, the second column, and the last column:

<?php $column = ($column == '') ? 'first' : (($column == 'first') ? 'middle' : (($column == 'middle') ? 'last' : 'first' )); ?>

This line of code needs to be within the loop, just before the post div.

To achieve more or less the same, you could obviously also use a counter variable and the modulus operator, as i have elaborated on in my earlier article ‘More-Than-Zebra style WordPress loop’. However, the above method is simpler and easier to apply within a single line of code.

The second step is to add this as a css class to the post div:

a – assume a theme without the use of ‘post_class()’; the typical opening div would look like:

<div class="post" id="post-<?php the_ID(); ?>">

This is changed into:

<div class="post <?php echo $column; ?>" id="post-<?php the_ID(); ?>">

b – in a theme using the ‘post_class()’, the new code would look like:

<div <?php post_class($column); ?> id="post-<?php the_ID(); ?>">

Third and last step: to tell the browser what to do with the new css classes, add some styles to style.css of the theme:

/* .first, .middle, .last styling of posts on home page for three column */
.first, .middle, .last { width: 32%; float:left; clear:none!important; }
.first { margin-right: 2%; clear:both!important; }
.middle { margin-right: 2%; }

Final details depend on the existing theme.

edit & ps:
if you just want to mark the first post in each row – for instance to add the ‘clear:both;’ and a different margin there – try to work with:
(example for 5 columns)

<div <?php $column = ($wp_query->current_post%5 == 0) ? 'first' : ''; post_class($column); ?> id="post-<?php the_ID(); ?>">