We hunt coyote exclusively at night. We prefer a cold snap to make sure they're hungry and dry weather with moderate wind.
We don't have huge numbers of coyotes and we spend about a half hour an hour in a spot. It can happen fast, as Brian notes, but it is surprising how many "last scans" turn up a coyote (or fox, which we also hunt.) We stay about 15 mins after the last calling.
If we draw a coyote (or fox) and shoot, we either keep the call going or turn it on.
When we move, if we aren't changing farms, we move about a half mile and call again.
I agree with Brian about an electronic caller, and even the Fox Pro Inferno, one of the smaller, less expensive models, is a great caller comparable to much higher end caller of not that long ago. For big terrain a bigger caller with twin speakers or remote speaker is helpful.
Any decoy helps keep a coyote focused on something other than on you, and decoys work on brighter nights. A very useful decoy can be made with a turkey or goose feather on a length of 20lb monofilament fishing line tied to a 3' or so bamboo garden stake stuck in the ground. I will flutter in even light breezes. Doesn't work on windless nights though, which are not preferred anyway.
We like to hunt with the call more or less upwind, and prefer a wide view of the terrain. Even though a coyotes nose is sharp, it pays to keep scanning your downwind side. The breeeze may follow a terrain feature or rise above an area, or maybe the coyote will just ignore your scent, who knows for sure what happens when. For sure though, coyotes and foxes have appeared on the downwind side, sometimes very close.
I understand that some guys out west with really open terrain will hunt with their caller down wind, and hope to shoot the coyotes(s) before they circle down wind. Which bears noting - many times a coyote or fox will be coming to the call but will will try to circle down wind of the call before going to it. I think a fluttering electronic or feather decoy helps keep a coyote from circling downwind since it keeps their attention and seems to be the prey that is or has been making all of those calls.
If the ranch has a dead pile for carcasses, it always bears a look. One farm my buds and I hunt has a single dead pile where anything that dies is dragged, and deer carcasses, etc. we catch a fox or coyote on it every so often.
The best way to learn how to predator hunt is to go with a bud, or get him to hunt your place with you. Cuts down on the learning curve.
JPK