How do I add vendor payment methods

The debit card and the cash method are both checks.  For the debit card, you can enter debit as the check number.  Just select assign check number to the ones that are debit card.

For cash, set up a cash QB bank account.  Use this cash bank account just as you would any other bank account - make deposits into it and use the write check function to "withdraw" cash from is.  When you pay bill, use the check method and select the cash bank account.  You can put money into this cash bank account in several ways.  I usually make deposit of a cash payment into the cash bank account and put the money in my petty cash box.  I sometimes get cash back from a deposit and put that in my cash bank account.