The best way is to add something to the cart and then view source so you can see all of the classes and ids to address in your stylesheet ...
Example:
<!--// bof: shoppingcart //-->
<div class="leftBoxContainer" id="shoppingcart" style="width: 180px">
<h3 class="leftBoxHeading" id="shoppingcartHeading"><a href="http://www.hotdealspot.net/index.php?main_page=shopping_cart">Shopping Cart</a></h3>
<div id="shoppingcartContent" class="sideBoxContent"><div id="cartBoxListWrapper">
<ul>
<li><span class="cartOldItem">1ea.- </span><a href="http://www.hotdealspot.net/index.php?main_page=product_info&products_id=4"><span class="cartOldItem">Discovery Channel 20th Anniversary 5 DVD Collection</span></a></li>
</ul>
</div><hr /><div class="cartBoxTotal">$15.15</div><br class="clearBoth" /></div></div>
<!--// eof: shoppingcart //-->
Now you can find the existing classes or add them to your stylesheet for your template and customize them based on the id to specifically address the shopping cart sidebox and not the other sideboxes ...