Apple had shown many Reward Cards and Credit Cards in the last WWDC but the fact is that there are only few reward cards/loyalty cards which can be added to your Apple Wallet right now. More will be coming by this fall as I have read somewhere online.
They all work differently.
For example in case of Starbucks and DD,
1.) Buy gift cards (or if you have then simply add them) from respective stores. Minimum amount for Starbucks is 10 $ and Dunkin' Donut is 5 $. You can use them to pay for your own coffee.
2.) Make accounts for both stores online or via App Store applications.
3.) Add your respective gift cards in both applications.
4.) For DD, select "My Card" on bottom left corner in mobile application and add your gift card over there.
5.) For Starbucks select "PAY" option on top left corner of the mobile application and add your gift card over there.
6.) After that you will see an option to add them in your wallet in respective application.
In case of Walgreens,
1.) You just need to add your reward card in it's iOS application on your account.
2.) Go to Balance Rewards on the home screen of the application.
3.) You will see your Walgreens balance rewards there.
4.) Select "Add to Passbook" below it. (Yes. App is still showing passbook instead of wallet.)
Sometimes you will see blank screen on your Walgreen home screen. In that case delete the app and reinstall it. This will work.
I will let you know about more updates as they comes out.
Hope so this is helpful to you.
Thank you.