Keep your elbow pinned to your hip, your forearm perpendicular to your body, and your palm facing the sky. Then push hard with your back leg just like you would when you're swinging for a line drive, which makes you fire your hips through, which makes you fire your forearm through, which makes you snap your wrist and eject the disc.
Your body becomes a whole series of levers, just be sure to have them all back, cocked, and loaded to get triggered by the previous lever. If you do it in order you build up a ton of force with minimal movement. If you don't do it in order the energy isn't efficiently transfered through your body. Ie: If you fire your arm through before your hips then the force from your hips and legs doesn't get into the throw.
In the end it should feel like you're pushing hard with your legs and hips and your forearm and wrist just fire through on their own because they don't have a choice. So you're forearm basically just becomes a lever that gets rocketed through by your hips. That Sarah Hokom video is a perfect example. Watch her thighs flex and propel everything through.