I found my own answer in the Codex.
In my use case scenario:
$blog_terms = wp_get_object_terms( $post->ID, 'blog' );
if ( ! empty( $blog_terms ) ) {
if ( ! is_wp_error( $blog_terms ) ) {
foreach( $blog_terms as $term ) {
echo '<p>' . __( 'Associated Blog: ', 'wys' ) . '<a href="' . get_term_link( $term->slug, 'blog' ) . '">' . $term->name . '</a></p>';
}
}
}