That page describes their AstraZeneca & Me program & eligibility requirements, and has a link to their other programs.
Basically, the program is for people who have no drug insurance; for people with an insurance co-pay; or those who have a state or federal program (e.g. Medicare Part D or Medicaid or a state program) and who spend more than 3% of their income on prescription drugs (if you have too much income but spend more than 3%, apply anyway - you'll get a denial letter, then you need to appeal showing that you spent more than 3%).
I found out about this program from my doctor re Symbicort - and the brochure says they'll pay 100% of the first month's prescription, and 75% (up to $75) of the next 11 months refills.
The program apparently covers many of their products - but I'm not sure if it covers all. The full list of their drugs is here http://www.astrazeneca-us.com/our-medicines/
For people without Medicare, Medicaid or a state program:
To enroll online https://www.patientfeedbackprogram.com/astsym/
or call 1-800-352-8906 or call 1-888-800-0669 and when it asks for info from your card, choose the option for "I don't have a card".
If you have Medicare Part D or Medicaid or a state program, call 1-800-957-6285.
AstraZeneca's page listing other sources of prescription assistance