Discover is a very conservative lender. They generally like to see at least a few years of your own credit (ie not "piggybacking" as an authorized user on someone elses account).
Having said that; however, I have been reading lately about people with iffy credit (scores under 700) being approved for a low-limit, high APR Discover Card. Your mileage may vary (YMMV).
Discover has a pre-approval function on their website: https://www.discovercard.com/cardmembersvcs/acqs/app/chooseMyOffer/findMyOffer?ICMPGN=STL_CC_FMO
you would enter the requested information and it would result in a soft inquiry-this will not hurt your credit and only you would see this inquiry. Discover may or may not pre-approve you for something. Please remember that even if they do pre-approve you, this is not a guarantee for credit.
Can you tell us more about your overall credit file? So...you don't currently have a credit card? Do you have any installment loans like a car loan, student loan, mortgage or personal loan? Are you a student? If you are currently enrolled in a degree program at an accredited 4-year college or university, you may be able to qualify for a student card.
Discover is not really a first-time credit card issuer (with the exception of possibly a student card). They generally like to see a few credit cards on file that are at least a few years old. You are shooting for the stars right off the bat. You may need to build for a few years before you get a Discover or Amex.
I would recommend Capital One and maybe a secured card from Bank of America. After a year or two of making on-time payments and keeping your balances low, you should be able to apply for the Amex and Discover with a good chance at being approved. Remember to only apply for credit when you really need it and try to keep your Experian inquiries low.