Multiple category columns and post counting list in wordpress Homepage

<?php
$args = array(
    'show_option_all'    => '',
    'orderby'            => 'name',
    'order'              => 'ASC',
    'style'              => 'list',
    'show_count'         => 1, // 1 is true and 0 is false
    'hide_empty'         => 1,
    'use_desc_for_title' => 1,
    'child_of'           => 0,
    'feed'               => '',
    'feed_type'          => '',
    'feed_image'         => '',
    'exclude'            => '',
    'exclude_tree'       => '',
    'include'            => '',
    'hierarchical'       => 1,
    'title_li'           => __( 'Categories' ),
    'show_option_none'   => __('No categories'),
    'number'             => null,
    'echo'               => 1,
    'depth'              => 0,
    'current_category'   => 0,
    'pad_counts'         => 0,
    'taxonomy'           => 'category',
    'walker'             => null
);
wp_list_categories( $args );
?>

Put the codes anywhere you want to display it,
If you don’t want to display post count , keep 'show_count' => 0 .

For CSS li design, just try it yourself with cool icons. Hope this help you.

You can learn more about categories here:
http://codex.wordpress.org/Template_Tags/wp_list_categories
http://codex.wordpress.org/Template_Tags/wp_dropdown_categories