Many people see coyotes and are in range to shoot them, but they miss. These are some of the top reasons why people miss a shot at a coyote or predators (some of this doesn't just apply to predators but to all animals).

Eleven Reasons for missing a Coyote
1) Too much scope - Many people think that the more scope power the better. This isn't always true. When you have too much scope power, you'll miss a shot at a coyote that surprises you at a close range. To prevent this always keep your scope at a low magnitude and increase it if needed.
2) Not having a rest - Shots at coyotes can be up to 300 yards or 400 if your really good. Not having a rest will make your gun wobble uncontrollably these longer ranges. Getting some sort of rest is a must if you are serious about coyote hunting. You can by one at a store or make you own.
3) Can't hit 'em while they're running - All your shots at a coyote won't be while he is standing still. Be able to handle the running shot. Great practice for this is flushing out rabbits with a .22 or other similar caliber.
4) Forgot trajectory - At 200 yards a rifle bullet won't still be flying straight it will start to dip. Many times people when they are hunting forget about this and their shot goes low. To prevent this practice, practice, practice. Practice at different yardage to figure out you trajectory.
5) It's windy - With almost all shots over 100 yards the wind has to be taken into account. Just a little wind can move your bullet a couple inches. This could be the difference in a clean kill or a couple hours of tracking.
6) Closed lanes - If you only have a small opening to shoot at a coyote your shot will be hurried and off target. To prevent this make sure your shooting a lanes are clear and your have lots of open space.

7 )Didn't pick a spot - This is a frequent occurrence among people. They tend to aim at just the general vital area instead of picking a spot to shoot. Practicing picking a spot while shooting will greatly increase your kills.
8) Haven't practiced - If you go into the coyote season without shooting your gun at all except for the weekend before. You are going to be a pretty poor shot and will miss some that you should have had.
9) You don't understand coyotes - Lots of hunters don't understand coyote behavior and the coyote will surprise the hunter when he sprints towards the rabbit call like they sometimes do (unlike a bobcat which stalks its prey).
10) Your butt hurts - If you don't have a comfortable seat you won't be able to stay on a stand as long and you will miss many opportunities. Get a comfortable hunting seat and that problem should be taken care of.
11) You're flinching - This is a big reason why younger shooters miss. This can be because you have a gun that is too big or because your gun is too loud. You can help prevent these problems by buying a recoil pad and ear muffs.

Unlike most animals, to hunt coyotes you need to either bait them or call them in. Since baiting is illegal in a lot of states, I'm going to talk about calling coyotes.

The first step to calling coyotes is making sure there are coyotes in the close proximity. This can be done by scouting the land and looking for tracks or by asking landowners where they usually see coyotes.

The second step is setting up. You want to set up facing the wind. You also want the coyotes coming from in front of you. You will need to be in a spot that blurs your outline and provides clear shooting lanes.

Third you need to be camoflauged to fit the environment. If there is snow everywhere you should be wearing a green leafy camoflauge suit, you should be wearing something white.

Last but not least is the calling itself. The sound trying to be mimicked is the sound of a rabbit in distress. Almost all commercial calls will make this call fine. Electronic calls provide some advantage, as they can be set up away from where you are, so the coyotes don't see you. (Electronic calls are illegal in some states so check your hunting laws.) You want to call for about 10-15 seconds then wait 2-5 minutes before calling again. You should stay put for about 30 minutes until moving to your next stand.

Coyote hunting can be fun and exciting. It also gets rid of many pests that farmers hate. Calling is key to coyote hunting, but the set up for coyote hunting is more important. You can be the best coyote caller in the world, but if you aren't set up right you won't kill a single coyote.