How do you hammer a screw without hitting your finger all the time?

You don't hammer screws. You hammer nails.
The trick is to hold the nail just below the top. Then start tapping very gently. After a few taps the nail will stand up on its own. Then gently increase the strengh of the taps. This will alow your brain to get used to where the nail is. Also the nail will become stronger the further into the wood it goes.
The most important thing is to be patient. Don't try to knock it in in three blows.

If it's in a difficult place to hold the nail, I hold the nail in place with a small pair of pliers. Some people do hammer screws, just to put them in at the right place and then continue with a screwdriver.