How do I properly apply chamois cream?
There's no right/wrong answer.  Just make sure you have some sort of towel available so you can wipe your hands before riding.

What I generally do is place dabs on the chamois and rub the sides together to spread it around -- keeps the hands relatively clean and doesn't require a separate applicator.  Some people prefer to rub it on their butt.

I don't use a lot -- maybe a half ounce (about 15 cc, IIRC).  Others use much more, maybe 2 oz.