<?php
// passing name/value pairs
$smarty->assign('Name', 'Fred');
$smarty->assign('Address', $address);

// passing an associative array
$smarty->assign(array('city' => 'Lincoln', 'state' => 'Nebraska'));

// passing an array
$myArray = array('no' => 10, 'label' => 'Peanuts');
$smarty->assign('foo',$myArray);

// passing a row from a database (eg adodb)
$sql = 'select id, name, email from contacts where contact ='.$id;
$smarty->assign('contact', $db->getRow($sql));
?>

These are accessed in the template with

{* note the vars are case sensitive like php *}
{$Name}
{$Address}
{$city}
{$state}

{$foo.no}, {$foo.label}
{$contact.id}, {$contact.name},{$contact.email}