Each patient can grow 12 plants total, or designate a caregiver to grow them on their behalf.
A caregiver can have up to 5 patients, so 60 plants, plus another 12 for themselves if they happen to be a patient as well as a caregiver. So the max is 72 plants at a single location.
In order to grow, you must live 25+ miles from the nearest dispensary. (Dispensaries won't open until July at the earliest, so it's likely that anyone getting their card within the first 6 months will be able to cultivate for the next year, at least.)