Home Page pagination

Hi,
you can use Code Snippets plugin and insert below snippet

function omega_child_theme_setup() {
	remove_action( 'omega_after_loop', 'omega_content_nav');
	add_action( 'omega_after_loop', 'omega_child_content_nav'); 

}
endif; // omega_child_theme_setup

add_action( 'after_setup_theme', 'omega_child_theme_setup', 11  );

function omega_child_content_nav() {
	global $wp_query, $post;

	// Don't print empty markup on single pages if there's nowhere to navigate.
	if ( is_single() ) {
		$previous = ( is_attachment() ) ? get_post( $post->post_parent ) : get_adjacent_post( false, '', true );
		$next = get_adjacent_post( false, '', false );

		if ( (!$next && !$previous) )
			return;
	}

	if ( is_singular() && !get_theme_mod( 'single_nav', 0 ) ) {
		return;
	}

	// Don't print empty markup in archives if there's only one page.
	if ( $wp_query->max_num_pages < 2 && ( is_home() || is_archive() || is_search() ) )
		return;

	$nav_class = ( is_single() ) ? 'post-navigation' : 'paging-navigation';

	?>
	<nav role="navigation" id="nav-below" class="navigation  <?php echo $nav_class; ?>">

	<?php if ( is_single() && get_theme_mod( 'single_nav', 0 ) ) : // navigation links for single posts ?>

		<?php previous_post_link( '<div class="nav-previous alignleft">%link</div>', '<span class="meta-nav">' . _x( '&larr;', 'Previous post link', 'omega' ) . '</span> %title' ); ?>
		<?php next_post_link( '<div class="nav-next alignright">%link</div>', '%title <span class="meta-nav">' . _x( '&rarr;', 'Next post link', 'omega' ) . '</span>' ); ?>

	<?php elseif ( $wp_query->max_num_pages > 1 && ( is_home() || is_archive() || is_search() ) ) : // navigation links for home, archive, and search pages ?>

		<?php
		// Don't print empty markup if there's only one page.
		if ( $GLOBALS['wp_query']->max_num_pages < 2 ) {
			return;
		}
		?>
		<?php if ( get_next_posts_link() ) : ?>
		<div class="nav-previous"><?php next_posts_link( __( '<span class="meta-nav">&larr;</span> Previous Posts', 'omega' ) ); ?></div>
		<?php endif; ?>

		<?php if ( get_previous_posts_link() ) : ?>
		<div class="nav-next"><?php previous_posts_link( __( 'Next posts <span class="meta-nav">&rarr;</span>', 'omega' ) ); ?></div>
		<?php endif; ?>

	<?php endif; ?>

	</nav><!-- #nav-below -->
	<?php
}

Then you can adjust the css to right aligned the “Previous Posts”

.nav-previous {
  float:right;
}

Did you activate your snippet? It works in our test.