This also drove me mad as I could not find a place to view my outstanding balances with due dates and a way to pay now BUT then I figured it out by accident as it is a bit obscure.
Do the following:
1) Click "TRIPS" on the main page top menu
2) Then click the "Show trip details" link underneath the picture of the place will be staying
3) On the "Trip Overview" screen - click on the picture of the place (directly above the "contact host" button)
4) A "You Reservation details" window will open - finally click "Payment & receipts"
And that is it but not at all straight forward to me....