I have multiple user and each user should have the option to upload some documents in his account.

I used this function in order to create a folder for each user at the registration process.

function create_user_dir($user_id) {
    $user_info = get_userdata( $user_id );

    $upload_dir = wp_upload_dir();
    $user_dir = $upload_dir['basedir'] . '/user_dirs/' . $user_info->user_login;

    wp_mkdir_p($user_dir);
}
add_action( 'user_register', 'create_user_dir');

Now I need to make the upload field, do you have any idea? Thanks