To select an invoice to process a payment against please enter the invoice number in the "Invoice ID" field. This field is an 'auto-complete' field which means that say if you have 12 invoices in your database, when you enter "1" into this field it will return a drop down list of all the invoices with "1" in its invoice id.
So invoices 1,10,11, and 12 will be returned if you enter "1". To select the required invoice either use the navigations keys on your keyboard and click enter on the invoice of use your mouse and click on the invoivce.
Once an invoice has been selected using the above process all the details for this invoice will be displayed in the 'Details' section of the Process Payment screen