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 :)

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.

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

See documentation:

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

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>

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(); ?>

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 );
?>

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.

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

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>

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 . ' ';} ?>">

If it is a category page,you can get id of current category by:

$category = get_category( get_query_var( 'cat' ) );
$cat_id = $category->cat_ID;

If you want to get category id of any particular category on any page, try using :

$category_id = get_cat_ID('Category Name');