Q: I don't used a credit card, so how do I update or download free apps

If you do not see a None option among the payment methods, you can redeem a $10 iTunes Gift card.

The following has information on how to change your payment method: Change or remove your payment information from your iTunes Store account (Apple ID) - Apple Support

The following has information on None as a payment method Why can’t I select None when I edit my Apple ID payment information? - Apple Support

Note at the top it gives the following quote (you can click on the link in the quote for further information):

If you don't want to use a credit card, you can use another form of payment, such as a gift card.