Best way to hunt coyotes? Depends what you mean by "best way"...

Most versatile way is calling. Most productive way (in my experience) is flushing/sight hounding, baiting behind that, calling 3rd. Most efficient? Trapping. Running dogs means you have to have dogs, and have to cover a lot of ground to flush out coyotes. Baiting requires a LOT of dedicated time managing your bait piles.

Most guys that hunt coyotes are calling them.

See these topics (and others) in the Predator Hunting Reference Section to help you along your way. If you have other specific questions, you can ask them there as well:

Plan of Attack: Duration, Location, Frequency

Scouting and Set Design

Easy answer is to scout a lot, know where the coyotes are actually living/traveling/hunting/denning, and hunt there. Plan your sets to lure coyotes to a preferred kill zone, then design your shooting position and approach based on that. Hunt from the ground, move as little as possible, and watch more than you call. If you have a hunting buddy, position them 50-100yrds downwind of your calling position, preferably with a shotgun backed up with a rifle.