How to display current post taxonomies and terms
Here is a modified code from the Codex (see link below) that will display all the taxonomies of the current post with attached terms: 
<?php 
// get taxonomies terms links
function custom_taxonomies_terms_links() {
    global $post, $post_id;
    // get post by post id
    $post = &get_post($post->ID);
    // get post type by post
    $post_type = $post->post_type;
    // get post type taxonomies
    $taxonomies = get_object_taxonomies($post_type);
    $out = "<ul>";
    foreach ($taxonomies as $taxonomy) {        
        $out .= "<li>".$taxonomy.": ";
        // get the terms related to post
        $terms = get_the_terms( $post->ID, $taxonomy );
        if ( !empty( $terms ) ) {
            foreach ( $terms as $term )
                $out .= '<a href="' .get_term_link($term->slug, $taxonomy) .'">'.$term->name.'</a> ';
        }
        $out .= "</li>";
    }
    $out .= "</ul>";
    return $out;
} ?>
This is used like this:
    <?php echo custom_taxonomies_terms_links();?>
Demo output
The output might look like this if the current post has the taxonomies country and city:
<ul>
    <li>  country:  
          <a href="http://example.com/country/denmark/">Denmark</a> 
          <a href="http://example.com/country/russia/">Russia</a> 
    </li> 
    <li>   city:  
           <a href="http://example.com/city/copenhagen/">Copenhagen</a> 
           <a href="http://example.com/city/moscow/">Moscow</a> 
    </li> 
</ul>
Reference
The original code example in the Codex:
http://codex.wordpress.org/Function_Reference/get_the_terms#Get_terms_for_all_custom_taxonomies
Hope this helps - I'm sure you can adapt this to your project ;-)
Update
But what if I want to display only some of them and not all of them?
  Also, I would like to name them myself instead of it giving taxonomy
  names with underscores. Any idea how can I achieve that?
Here is one modification to achieve that:
function custom_taxonomies_terms_links() {
    global $post;
    // some custom taxonomies:
    $taxonomies = array( 
                         "country"=>"My Countries: ",
                         "city"=>"My cities: " 
                  );
    $out = "<ul>";
    foreach ($taxonomies as $tax => $taxname) {     
        $out .= "<li>";
        $out .= $taxname;
        // get the terms related to post
        $terms = get_the_terms( $post->ID, $tax );
        if ( !empty( $terms ) ) {
            foreach ( $terms as $term )
                $out .= '<a href="' .get_term_link($term->slug, $tax) .'">'.$term->name.'</a> ';
        }
        $out .= "</li>";
    }
    $out .= "</ul>";
    return $out;
}