Adding Search Form and Simple Social Icons to Primary Navigation in Genesis. http://sridharkatakam.com/adding-search-form-simple-social-icons-primary-navigation-genesis/

functions.php

genesis_register_sidebar( array(
	'id'          => 'nav-social-menu',
	'name'        => __( 'Nav Social Menu', 'your-theme-slug' ),
	'description' => __( 'This is the nav social menu section.', 'your-theme-slug' ),
) );

add_filter( 'genesis_nav_items', 'sws_social_icons', 10, 2 );
add_filter( 'wp_nav_menu_items', 'sws_social_icons', 10, 2 );

function sws_social_icons($menu, $args) {
	$args = (array)$args;
	if ( 'primary' !== $args['theme_location'] )
		return $menu;
	ob_start();
		echo '<li class="search-social">';
		get_search_form();
		genesis_widget_area('nav-social-menu');
		echo '</li>';
	$social = ob_get_clean();
	return $menu . $social;
}

style.css

/* Adding Search Form and Simple Social Icons to Primary Navigation
---------------------------------------------------------------------- */

.nav-primary {
	margin-bottom: 20px;
}

input:focus::-webkit-input-placeholder { color:transparent; }
input:focus:-moz-placeholder { color:transparent; } /* Firefox 18- */
input:focus::-moz-placeholder { color:transparent; } /* Firefox 19+ */
input:focus:-ms-input-placeholder { color:transparent; } /* oldIE ;) */

.search-social {
	float: right;
	list-style-type: none;
	list-style-image: none;
	padding-top: 6px;
}

.search-social .search-form {
	float: left;
	width: auto;
	margin-right: 10px;
}

.search-social .widget-area {
	float: left;
	padding-top: 2px;
}

.search-social .simple-social-icons ul li {
	margin-bottom: 0 !important;
}

.search-social .simple-social-icons ul li:last-child {
	margin-right: 0 !important;
}

@media only screen and (max-width: 1024px) {

	.search-social {
		float: none;
		display: table;
		margin: 0 auto 20px auto;
	}

}

@media only screen and (max-width: 320px) {

	.search-social .search-form {
		float: none;
		margin-bottom: 20px;
	}

	.search-social .widget-area {
		float: none;
	}

}