If you are using another shopping cart system, or a Pay Now button, to receive payments, unfortunately the transactions will not automatically push through to Xero.
You will be able to download a Xero CSV recon report from your Transaction History page, which can then be uploaded to your Xero account tool, via the 'manually import a statement' link.
Any additional information you would like to add for the transactions, for example additional information on the order stored on your shopping cart, can be added to this Xero CSV, and included along with the transaction data.