Recording a payment will not process the payment through a payment gateway (i.e. apply a charge to a credit card or a debit to a bank account). Recording a payment will only add the payment to the account.
Under the Payments heading on the left, click the icon
Under the Add Payment heading on the right enter the payment details
Once the payment details are populated you can click on the invoices on the Unpaid Invoices tab to select which invoices to apply the payment to (assuming the payment is not set to auto-disburse). After selecting an invoice enter the disbursement amount in the Disburse Amount field that appears. Any amount remaining to disburse will be shown at the bottom of the panel in the Amount left to disburse field