There are lots of ways to call coyotes. Most of the above are likely the least effective methods I've ever heard of.
Sure they can work, I suppose, but it's not all that likely to produce a high number of coyotes.
I started calling back in around 1976 when I was a kid. I hunted with a couple of mouth calls hanging around my neck, and a .243 Win to shoot them with. I wore good camo, and I killed an awful lot of coyotes.
Set up, call for about 10-40 seconds with the mouth call, then wait a minute or so. Then repeat that sequence, more or less, over a period of about 15-20 minutes. If nothing shows up, go a mile or so, set up, and call again.
With a mouth call, try to mimic a histercal baby crying. I try to make my call sound like a rabbit that something got ahold of, but can't quite kill it. I'll get the call screaming one second, whimpering the next, and put some crying into it too. Believe me, it drives coyotes crazy.
When you set up, sit in front of a bush, clump of grass, rocks, or whatever to break up your outline. Wear good camoflage (but you don't have to go all out. I use day-desert military fatiques and they work great).
Pay attention to the wind. Coyotes coming to a call will oft-times circle downwind. This may or may not be because they suspect a shooter to be there. Coyotes naturally hunt with their nose, and if they don't know exactly where you are, they'll circle downwind to catch the scent of what they're looking for. You can't stop them from trying to do this, so try to set up so that you or a calling buddy can shoot that direction. Forget about cover scents. I've even used skunk scent, and they'll still smell you if they get downwind.
Over the years, I've used electronic calls of various flavors. They'll call coyotes well enough. I don't think you have to spend big bucks on a caller though. A walkman type tape player plugged into a horn type speaker will work pretty well. I'm convinced I can outcall the e-callers I've used using mouth blown calls, but I have a lot of experience with them.
Calling coyotes should be a learning process. The more you do it, the more you can learn from your own experience. Going at it casually (read sloppy) can be entertaining, but it won't generally produce very many coyotes. Dumb coyotes don't last long. They either get killed, or they get an education.
Daryl