Thanks for the nice tutorial, Ken!
To output halftones directly from Illustrator (or Corel, for that matter), you'll either need a RIP, a postscript printer, or use Ghostscript.
Here's how in Photoshop:
1. If you're working with 4-color, duplicate your file, open the duplicate, make sure the layers are flattened, then select Split Channels. This will give you a file for each of the four colors as grayscale.
2. Select one of the 4 files, and in the Image menu at the top, select Mode, and then Bitmap. You'll get a dialog box asking a method to convert, and you'll select Halftone. Press Okay, and you'll get another dialog box where you can specify your screen angle, lines per inch, and dot shape. Make your choices and save the file. Additionally, once you know what screen angle, dot shape and linescreen you want to use for that particular color, you can record an action for each separation and just play it for that color after you split the channels . . . pretty much push-button halftone seps the next time you need to make halftones. You need an action for each color since the screen angle will change for each one, unless you're doing spot color or simulated process. You'll need to make additional action sets for different linescreens (45, 50, 55, etc.) if you use different ones for any reason.