First of all you need to get the paged query variable and pass it to your main query args:
//Protect against arbitrary paged values
$paged = ( get_query_var( 'paged' ) ) ? absint( get_query_var( 'paged' ) ) : 1;
$args = array(
'post_type' => 'post'
'paged' => $paged,
);
Then you have to add the following code at the place where you want the pagination to appear:
<?php
$big = 999999999; // need an unlikely integer
echo paginate_links( array(
'base' => str_replace( $big, '%#%', esc_url( get_pagenum_link( $big ) ) ),
'format' => '?paged=%#%',
'current' => max( 1, get_query_var('paged') ),
'total' => $post_query->max_num_pages
) );
?>