If you want to automatically send an email to users when they put items in their shopping cart and never complete checkout, you can use the purchase API call to do this.
Simply make the purchase call whenever the user adds an item to their shopping cart, as well as when they complete final checkout. Each time they add an item, use the reminder_time and reminder_template optional parameters. If no more activity happens on that shopping cart, the reminder_template will get sent.
You can also remind people about what's currently in their cart from other emails that you are sending, such as daily sale emails. The entire incomplete purchase is always stored in {profile.purchase_incomplete}. For example, you could put a block like this at the top of your campaign email.
{if profile.purchase_incomplete}
<p>The following is currently in your cart:</p>
{foreach profile.purchase_incomplete.items as i}
{i.qty} {i.title} ${number(i.price/100,2)}<br/>
{/foreach}
<a href="http://link/to/your/site">Complete Checkout</a>
{/if}
Only those users who have abandoned carts will get that special block of content.