When coupons or promo codes are available, you can redeem them here: https://www.netflix.com/redeem . For existing Netflix customers you must be signed in to your account to redeem your promotional gift. For new customers, you will be prompted to create an account before you are able to redeem your gift.
You need to enter some sort of payment to activate your free trial. This payment method won't be charged unless you fail to cancel your subscription before your free trial expires. Like you mentioned you can use a credit card (visa, mastercard, amex or discovery) or Paypal; but, you can also pay with a Netflix gift card if you prefer.
To get a 1 month free trial go to netflix.com and click on the red "Join Free For A Month" button. Next enter your email address and create a Netflix password. Finally you will need to enter some method of payment that can be used if you would like to continue using Netflix after your free trial is over.
Yes, you should still be able to log-in to your account with your old Netflix log-in information. Also, Netflix does save your account info for at least a year after you cancel your subscription. So you can still find all of your preferences, saved movie and TV queues, ratings and other custom information that you had already put into the system. But you need to become a paying member again to access all of this information. Right now the basic plan is $7.99 a month + first month free. Hope this helped!