The beauty of hybrid is that you do whatever you want, lol. Create a document whatever size you want (the small standard size is 4.25x5.5, but you can really do whatever you want). Create your card in that document. You can either do shadows and everything in the document like you would a layout, and then flatten and print. Or you can size everything the way you want, and then print each piece separately. Totally a personal preference.
You can print on whatever you want. Regular cardstock, glossy photo paper, matte photo paper, etc etc. You print it out as you would a regular photo (or at least that's what I do). Alternatively, some people like to print out as 4x6 and use an outside printer like Walmart or Walgreens or whatever. Same principle, just different method of printing.
You adhere it with glue or a tape runner or glossy accents or mod podge. Whatever you're comfortable with. You embellish with whatever you want. Print and cut out digital piece, or use stuff from your real life stash.
Really, you do whatever you want, lol. There are no "rules" for hybrid.