PHP

Displaying the category name of a custom post type

<?php
    $terms = wp_get_post_terms( $post->ID, 'PLACE-HERE-YOUR-TAXONOMY');
    foreach ( $terms as $term ) {
       $term_link = get_term_link( $term );
       echo '<a href="' . $term_link . '">' . $term->name . '</a>' . ' ';
       }
  ?>

Get the post category if you have a custom post_type

<?php
/* FIRST
 * Note: This function only returns results from the default “category” taxonomy. For custom taxonomies use get_the_terms().
 */
$categories = get_the_terms( $post->ID, 'taxonomy' );
// now you can view your category in array:
// using var_dump( $categories );
// or you can take all with foreach:
foreach( $categories as $category ) {
    echo $category->term_id . ', ' . $category->slug . ', ' . $category->name . '<br />';
}