1. Add the following function in your theme template.php

function <theme>_get_user_nodes_count($uid) {
  $query = db_select('node', 'n');
  $query->condition('uid', $uid, '=');
  $query->condition('status', '1', '=');
  $query->addExpression('COUNT(1)', 'count');
  $result = $query->execute();

  if ($record = $result->fetchAssoc())
    return $record['count'];
  
  return 0;
}

2. So you could retrieve the node count by calling

<theme>_get_user_nodes_count($uid)

If you only want to count the number of nodes of a specific content type use the following piece of code in template.php instead

function <theme>_get_user_nodes_count($uid) {
  $query = db_select('node', 'n');
  $query->condition('type', '<content-type>', '=');
  $query->condition('uid', $uid, '=');
  $query->condition('status', '1', '=');
  $query->addExpression('COUNT(1)', 'count');
  $result = $query->execute();

  if ($record = $result->fetchAssoc())
    return $record['count'];
  
  return 0;
}

Done =)

Next: Drupal 7 – Get the number of comments by user

Reference: Drupal Forum – Post count (x)/comment count (x) on user profile page