If it's the one you signed up for with your hosting account, DH takes care of it for free.
If it's another domain, with DH or another registrar, it depends on your agreement. If you chose to automatically renew it, they should just bill the card you used the first time. If not, they generally send out 90, 60, and 30-day reminders.
I wouldn't assume it's automatic unless you're certain you specified that option somewhere, or it's your free DH domain.
This is also assuming that you only registered it for one year. Some registrars default to two unless you specify a longer/shorter period.
If none of this sound right, it might be a good time to check your whois info and make sure that your contact info is valid--especially your email address.