First off, welcome to the site, BigBlue!!
We have a great bunch of guys here who are experts in their own right. Our website is growing fast, so hopefully you'll be getting some great responses.
Leglifter is correct. LEARN, LEARN, LEARN, all you can about the coyote and coyote hunting. Visit websites (we have a nice list of them on our Links page), read articles, and hook up with someone who is good at coyote hunting (we have some of those in this organization too).
Scout, scout, and scout even more. Can't shoot a coyote if they aren't in the area.
Practice and learn the art of calling, whether it be handheld or electronic, practice and learn the sounds that will attract coyotes.
Make sure you're using the right setup. Gun, shells, caller(s), full camo, and other incidentals.
Watch videos and DVDs of coyote hunting. Attend calling seminars (we have one coming up soon with a nationally known caller) whenever you can.
Join people and/or organizations who can help you do those things.
Best of luck. A hunted eastern coyote kill is a trophy!! Go get'em!!