How to determine if I'm on the first page of pagination?

I was looking for a simple way to determine whether or not to use the posts_nav_link() function and all solutions I found online were either too complex or unreliable. For example, many people suggested using the $paged global variable, but I found that this variable returned the same value for the first page, even when the first page was the only page!

So, I dug into the wp-includes/link-template.php file, and found that the posts_nav_link() function simply outputs the return value of another function:

/**
 * Display post pages link navigation for previous and next pages.
 *
 * @since 0.71
 *
 * @param string $sep Optional. Separator for posts navigation links.
 * @param string $prelabel Optional. Label for previous pages.
 * @param string $nxtlabel Optional Label for next pages.
 */
function posts_nav_link( $sep = '', $prelabel = '', $nxtlabel = '' ) {
    $args = array_filter( compact('sep', 'prelabel', 'nxtlabel') );
    echo get_posts_nav_link($args);
}

Using this knowledge, we can create a simple and effective way to determine whether or not we need to add links to navigate between pages:

$posts_nav = get_posts_nav_link();
if(empty($posts_nav)) {
    // do not use posts_nav_link()
} else {
    // use posts_nav_link()
}

Originally posted on my blog here.

if you only want to know that you're on the first page of a paginated page try is_paged():

if ( !is_paged() ) {
  // first page of pagination
}

// get current page we are on. If not set we can assume we are on page 1.
$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
// are we on page one?
if(1 == $paged) {
    //true
}