Screen printers used to reproduce full-color images with a kind of paint-by-number approach using spot colors.

Modern screen printers can print fairly high-resolution halftones in 4-color process, but you should talk to your (or your client's) screen printer and find out what his/her requirements are (and what substrate they're printing on--your artwork looks like it might go on a vehicle). Also, ask your client if they want "simulated" process color for an intentional retro look.

"Simulated process" means setting it up with four colors, but the colors aren't CMYK, and typically there's an underlay color because the substrate (usually a dark T-shirt) isn't white. In your case, you could have black, two shades of brown, and white. Check out this article about it, and/or google "simulated process separations."

Also, it's probably worth mentioning that antialiasing is a bad idea in printing in general, so you'll want a version (if you don't already have one) at a higher resolution without antialiasing. You'll need to know the final size they're printing this at.

There probably are plug-ins to streamline this process, but essentially you want to end up with a Photoshop file with a channel for each color. When you make a new channel, you can pick the color and screen angle, and then you can move the appropriate parts of the image into the new channel.

Good luck!

Ideally you'd be communicating directly with the printer. They want what they want and it's easy to get incorrect results when translating through the client.

Found this:
http://www.quikseps.com/index.php

If they want Illustrator files, it sounds like vector graphics, and then Photoshop wouldn't work. I second the idea of talking straight to the printers to find out what they want and how many colours are there at your disposal.