get_* functions are return functions. They don't actually print anything. Given your code example, all you should need is an echo statement:

<?php 
global $post;
$category = reset(get_the_category($post->ID));
$category_id = $category->cat_ID;
?>

<a class="button" href="<?php echo get_category_link( $category_id ); ?>">&larr; Back to Portfolio</a>

ALTERNATIVE: The best way of doing this would be to keep everything in your loop for reuse in single or archive views, combined with the use of wp_get_post_categories. This is untested, but it should get you started with a general-use method of listing categories associated with a given post or set of posts:

<?php
if(have_posts()) : while(have_posts()) : the_post();
    $cats = wp_get_post_categories($post->ID);
    if($cats) : foreach($cats as $cat) : $category = get_category($cat);
    ?>
    <a class="button" href="<?php echo get_category_link($category->cat_ID); ?>">&larr; <?php echo $category->name ?></a>
    <?php
    endforeach;endif;
endwhile;endif;
?>

You are using the get_the_terms() but this function is used to get the custom taxonomies.

Use the function get_the_category(); inside the WordPress loop and pass the get_the_ID() function which will get the current post ID in the loop.

get_the_category(get_the_ID());

                <?php
                  $args = array(
                    'post_type' => 'work',
                    'posts_per_page' => '9'
                  );
                  $work_loop = new WP_Query( $args );
                  if ( $work_loop->have_posts() ) :
                    while ( $work_loop->have_posts() ) : $work_loop->the_post();
                      // Set variables
                        $cat_ids                = get_the_ID();
                        $cat_names_array        = get_the_category($ids);
                        $work_category           = get_the_category( get_the_ID() );
                        $work_title             = get_field( 'work_title' );
                        $work_main_image        = get_field( 'work_main_image' );
                        $work_link              = get_field( 'work_title' );
                        $work_about             = get_field( 'work_about' );
                        // $work_category = get_the_terms( the_post()->ID, 'taxonomy' );
                      // Output
                      ?>
                      <a href="<?php echo $work_main_image['url']; ?>" class="single_item link <?php foreach ( $work_category as $key => $value) { echo $value->category_nicename . " "; } ?> col-md-4 col-sm-6 wow fadeInUp" data-wow-delay="0.3s">
                        <img src="<?php echo $work_main_image['url']; ?>" alt=""> 
                    </a>
                    <?php
                      endwhile;
                    wp_reset_postdata();
                  endif; 
                ?>

Cheers :)

You need to get the category object and then use a foreach loop to build your list.

This should work for you:

<?php $categories = get_categories(); ?>
<nav>
  <?php foreach ($categories as $category):?>
    <a href="<?php echo get_category_link($category->term_id); ?>" class="nav-link" id="<?php echo $category->name;?>"><?php echo $category->name;?></a>
  <?php endforeach; ?>
</nav>

Sounds like you may want get_category_link - something like:

$categories = get_categories();
foreach ($categories as $cat) {
    $category_link = get_category_link($cat->cat_ID);
    echo '<a href="' . esc_url($category_link) . '" title="' . esc_attr($cat->name) . '">' . esc_html($cat->name) . '</a>';
}

should print out the links to the categories for you.

One these three should do the job for you...

1. Function: the_category();

News su <?php the_category(', '); ?>

Displays as:

News su WordPress, Computers, Blogging

And if only a single category is assigned to a post, it shows up like this:

News su WordPress

2. Function: get_the_category_list();

<div id="pagine"><?php echo get_the_category_list(); ?></div>

Displays as:

<div id="pagine">
    <ul class="post-categories">
        <li>
            <a href="http://example.com/category/wordpress/" title="View all posts in Business" rel="category tag">WordPress</a>
        </li>
        <li>
            <a href="http://example.com/category/computers/" title="View all posts in Business" rel="category tag">Computers</a>
        </li>
    </ul>
</div>

And if only a single category is assigned to a post, the output would be like this:

<div id="pagine">
    <ul class="post-categories">
        <li>
            <a href="http://example.com/category/wordpress/" title="View all posts in Business" rel="category tag">WordPress</a>
        </li>
    </ul>
</div>

3. Function: single_cat_title();

If you want to show just one category (category with the lowest ID will be shown) no matter how many categories are assigned to a post, use something like this:

<div id="pagine">
    <ul>
        <li>
            <?php
                $category = get_the_category();
                echo '<a href="'.get_category_link($category[0]->cat_ID).'">News su ' . $category[0]->cat_name . '</a>';
            ?>
        </li>
    </ul>
</div>

The above code always shows one category, like this:

News su WordPress

So, given the codes (and what each does), suit them to your needs.

If you want to do this on post page you can add something like the following to your single.php file of your theme.

<div class="meta">Posted in: <span><?php the_category(', ') ?> </span></div>

Pass the category id into get_category_link():

<?php
$category = get_the_category();
$link = get_category_link( $category[0]->term_id );
?>

Update Outputting in template:

<?php
$category = get_the_category();
$first_category = $category[0];
echo sprintf( '<a href="%s">%s</a>', get_category_link( $first_category ), $first_category->name );
?>

Use:

get_category_link( $category_id );

See:

https://codex.wordpress.org/Function_Reference/get_category_link

In your specific case:

<?php
global $post;
$categories = get_the_category();

    foreach ($categories as $category) :

       $exclude = get_the_ID();
       $posts = get_posts('posts_per_page=4&category='. $category->term_id);

        foreach($posts as $post) :
         if( $exclude != get_the_ID() ) { ?>

                <a href="<?php the_permalink(); ?>" title="<?php the_title(); ?>" class="post c-1"> Link to actual post</a>

    <?php } endforeach; ?>

<a href="<?php echo esc_url( get_category_link( $category->term_id ) ); ?>" title="View all" class="btn border"><i class="i-right-double-arrow"></i> View all <?php echo $category->name; ?></a>
<?php  endforeach; wp_reset_postdata(); ?>

You can use get_queried_object(), which will return category object.

See documentation:

https://codex.wordpress.org/Function_Reference/get_queried_object

There is a function called get_category_link() which might be helpful for you. This will be able to generate an appropriate link without having to hard-code it, except for the category name or ID.

Examples from the Wordpress Codex:

<?php
    // Get the ID of a given category
    $category_id = get_cat_ID( 'Category Name' );

    // Get the URL of this category
    $category_link = get_category_link( $category_id );
?>

<!-- Print a link to this category -->
<a href="<?php echo esc_url( $category_link ); ?>" title="Category Name">Category Name</a>

http://codex.wordpress.org/Function_Reference/get_category_link

From http://wordpress.org/support/topic/getting-category-slug-from-posts-in-the-loop:

<li class="<?php foreach(get_the_category() as $category) { echo $category->slug . ' ';} ?>">

Found the answer for something else but it also applies to my question.

add_action('woocommerce_archive_description', 'woocommerce_category_description', 2);

function woocommerce_category_description() {
    if (is_product_category()) {
        global $wp_query;
        $cat = $wp_query->get_queried_object();
        echo "CAT IS:".print_r($cat,true); // the category needed.
    }
}