1.) Left foot relatively flat in front. Different fighters have different footwork. Watch Frank Edgar's footwork and also the way he moves sideways. I have problems crossing my feet which is a big no no, but you're question is to throw a right cross which is fairly straight forward.
2.) Both fists up to chin level or higher if you like with elbows close to your chamber and chin tucked. This is for defensive, countering purposes and so you don't telegraph.
3.) You should be on the ball of your right foot. Then you pivot with your right foot when you launch your right cross utilizing your hip, abs, and core. This should all be in one motion.
Aim up. Try not to punch downwards, vulnerable to snapping your wrist. You're always aiming towards the chin of your opponent, eye, or nose even. If you're taller then you're crouching. Watch Nate, Nick Diaz, and Cole Miller. They're taller than most of their opponents so their knees are bent.
So flick out a jab with your left then pivot slightly with your right foot in the back and launch the cross. Easy.
Next up is your hook.
Learning a true hook will take some time. Most people don't throw it properly. It's not just a shoulder movement. It's really your entire core and you pivot with your lead leg instead.
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Maximus: For the glory of the Empire, sire.
Baked, not fried... the healthy choice.