$proxy = new SoapClient('http://magentohost/api/soap/?wsdl');
$sessionId = $proxy->login('apiUser', 'apiKey');

// Create a quote, get quote identifier
$shoppingCartId = $proxy->call( $sessionId, 'cart.create', array( 'magento_store' ) );

// Set customer, for example guest
$customerAsGuest = array(
    "firstname" => "testFirstname",
    "lastname" => "testLastName",
    "email" => "testEmail",
    "website_id" => "0",
    "store_id" => "0",
    "mode" => "guest"
);
$resultCustomerSet = $proxy->call($sessionId, 'cart_customer.set', array( $shoppingCartId, $customerAsGuest) );

// Set customer addresses, for example guest's addresses
$arrAddresses = array(
    array(
        "mode" => "shipping",
        "firstname" => "testFirstname",
        "lastname" => "testLastname",
        "company" => "testCompany",
        "street" => "testStreet",
        "city" => "testCity",
        "region" => "testRegion",
        "postcode" => "testPostcode",
        "country_id" => "id",
        "telephone" => "0123456789",
        "fax" => "0123456789",
        "is_default_shipping" => 0,
        "is_default_billing" => 0
    ),
    array(
        "mode" => "billing",
        "firstname" => "testFirstname",
        "lastname" => "testLastname",
        "company" => "testCompany",
        "street" => "testStreet",
        "city" => "testCity",
        "region" => "testRegion",
        "postcode" => "testPostcode",
        "country_id" => "id",
        "telephone" => "0123456789",
        "fax" => "0123456789",
        "is_default_shipping" => 0,
        "is_default_billing" => 0
    )
);
$resultCustomerAddresses = $proxy->call($sessionId, "cart_customer.addresses", array($shoppingCartId, $arrAddresses));

// add products into shopping cart
$arrProducts = array(
    array(
        "product_id" => "1",
        "qty" => 2
    ),
    array(
        "sku" => "testSKU",
        "quantity" => 4
    )
);
$resultCartProductAdd = $proxy->call($sessionId, "cart_product.add", array($shoppingCartId, $arrProducts));

// update product in shopping cart
$arrProducts = array(
    array(
        "product_id" => "1",
        "qty" => 5
    ),
);
$resultCartProductUpdate = $proxy->call($sessionId, "cart_product.update", array($shoppingCartId, $arrProducts));

// remove products from shopping cart, for example by SKU
$arrProducts = array(
    array(
        "sku" => "testSKU"
    ),
);
$resultCartProductRemove = $proxy->call($sessionId, "cart_product.remove", array($shoppingCartId, $arrProducts));

// get list of products
$shoppingCartProducts = $proxy->call($sessionId, "cart_product.list", array($shoppingCartId));
print_r( $shoppingCartProducts );

// get list of shipping methods
$resultShippingMethods = $proxy->call($sessionId, "cart_shipping.list", array($shoppingCartId));
print_r( $resultShippingMethods );

// set shipping method
$randShippingMethodIndex = rand(1, count($resultShippingMethods) );
$shippingMethod = $resultShippingMethods[$randShippingMethodIndex]["code"];

$resultShippingMethod = $proxy->call($sessionId, "cart_shipping.method", array($shoppingCartId, $shippingMethod));

// get list of payment methods
$resultPaymentMethods = $proxy->call($sessionId, "cart_payment.list", array($shoppingCartId));
print_r($resultPaymentMethods);

// set payment method
$paymentMethod = array(
    "method" => "checkmo"
);
$resultPaymentMethod = $proxy->call($sessionId, "cart_payment.method", array($shoppingCartId, $paymentMethod));

// add coupon
$couponCode = "aCouponCode";
$resultCartCouponRemove = $proxy->call($sessionId, "cart_coupon.add", array($shoppingCartId, $couponCode));

// remove coupon
$resultCartCouponRemove = $proxy->call($sessionId, "cart_coupon.remove", array($shoppingCartId));

// get total prices
$shoppingCartTotals = $proxy->call($sessionId, "cart.totals", array($shoppingCartId));
print_r( $shoppingCartTotals );

// get full information about shopping cart
$shoppingCartInfo = $proxy->call($sessionId, "cart.info", array($shoppingCartId));
print_r( $shoppingCartInfo );

// get list of licenses
$shoppingCartLicenses = $proxy->call($sessionId, "cart.licenseAgreement", array($shoppingCartId));
print_r( $shoppingCartLicences );

// check if license is existed
$licenseForOrderCreation = null;
if (count($shoppingCartLicenses)) {
    $licenseForOrderCreation = array();
    foreach ($shoppingCartLicenses as $license) {
        $licenseForOrderCreation[] = $license['agreement_id'];
    }
}

// create order
$resultOrderCreation = $proxy->call($sessionId,"cart.order",array($shoppingCartId, null, $licenseForOrderCreation));