How to do paging in the loop?

Try adding

'paged' => get_query_var( 'paged' ) ? get_query_var( 'paged' ) : 1, // this will get the right posts for the current page (i.e. if the user loads www.domain.com/blog/page/2 directly)
'posts_per_page' => '6'

to your $args and delete showposts

showpostsis deprecated.

From the Codex reference for WP_Query:

showposts (int) – number of posts to show per page. Deprecated as of Version 2.1 in favor of 'posts_per_page'.

Add Pagination links:

<?php next_posts_link( '&larr; Older posts' ); ?>
<?php previous_posts_link( 'Newer posts &rarr;' ); ?>