We're pre-paying with cashier's checks and wires usually a week or two before we recive invoices so I simply go into write a check, put all the relevant info in there, deleting the check number and typing in WIRE or Cashier's Check number, then under expenses I select accounts payable and the vendor under customer/job (and if it's a wire I add the fees under our bank fees account). Then when the invoice comes in I put it into the system, the go to pay bills and apply the credit to the bill.
Also if I'm paying for an invoice already in the system with a wire or cashier's check I usually still put the payments in the same way as above and apply the credit to the bill since the pay bills feature only lets me select check or charge.
And I also assume that if I pay with cash I follow the same procedures as above.