If you pay via PayPal or credit card, a link to requesting the invoice will appear automatically in your account in the Payment history tab section on the Billing & payments page. Invoices are available depending on whether the transaction is still pending and may take up to 72 hours to become available after it is completed.
To request an invoice to be sent to your email address simply click on the envelope icon on the right hand column of the "Payments History" table. Alternatively, you can download a Excel spreadsheet of all transactions using the link at the bottom of the table.
If you are having any issues with requesting your invoice or if it has not been generated, please contact Nexmo Support.