Here are two snippets for displaying the category name and displaying the category link in WordPress.
To display the name of the first category:
<?php $cat = get_the_category(); echo $cat->cat_name; ?>
0 displays the first category, so
1 will display the second category,
2 will display the third category, and so on.
To display a list of links to each category:
<?php the_category(', '); ?>
', ' serves as a separator when the post is included in more than one category.