Adding payments as time goes on is as easy as the steps in Getting Started. Deleting long term bills when you've paid them off is even easier.
To manage this tracking system month-to-month, each payment only has, at most, two steps...
Update the event when you get notification from your payees
Move the event after payment has been made.
Verify upon notification
Some bills are never the same amount or due on the same day. For these you'll want to get some sort of notification of this. Email, of course, is best but paper works too. I still get them both ways. When you get notified simply update the amount in the event and/or change the due date accordingly.
Update after payment
When a payment posts to your account (or you have reasonable assurance that it will) move the event to the appropriate date for the next month.
One final tip here...
If it's one of those I don't know how much the payment is going to be next month bills replace the cents with "??" when you move the event. This stands as a flag that you have not received notification of the actual amount for the next payment.