Fades & Half Tones

Hi Guys

 I recently started working with a screen printer, re-drawing the scraps of paper his customers give him into nice clean vector art. But I am struggling with my half tones.

 What is the best was to create a half tone for screen printing?

 This is the image, it will be a one colour (white) print on a black t-shirt. I just need to get my half tones correct or it will look like crap!

 Any help would be greatly appreciated!