Overcalling is the biggest mistake new coyote hunters make. Going out into the woods and randomly hollering for coyotes is generally not a great idea. If you do call be sure to set-up on high ground, not in a hole or depression. Visibility is key.
I used to own and manage several thousands of acres and did no limit no season varmint killing as a side job. I killed coyotes on more days than I didn't kill them for nearly 10 years. Takes learning and patience. You need to know where they are, their habits, their main travel routes, hunting/feeding areas, etc. Being able to spot and locate dens, etc.
In general it takes years to learn to kill coyotes effectively. I'd recommend getting setup with somebody who has experience in your local area if possible.
The quickest way to "get kills" is calling in areas where they frequent, but using the right calls and what time of day is key. Coyotes are smart and will quickly learn that your calls and decoys are a threat instead of an opportunity. You can and will have success at first, but long term, all you're doing is educating them in a bad way. Do not overcall or overhunt a small set of woods or fields, this is a losing battle.
Spot and stalk or "run and gun" via side by side or vehicle is the best way to kill them regularly (meaning dozens per month minimum). Local cattle ranches or BLM/State land that has cattle or other livestock grazing it are the best places to kill.
Watch for birds, magpies, gray jays, ravens, vultures, etc as a tipoff to fresh kill locations. Approach carefully and then watch the area for returning coyotes. If you are in an area with a high population of rabbits and squirrels or other small game you are usually in a great area to find coyotes.
Don't hunt for coyotes like you do for deer or elk. Hunt as if you were hunting for another deer/elk hunter. Anticipate differently and don't ask yourself what would a deer or elk do in this situation, but rather what would an elk or deer hunter do in this situation.
Once you kill a coyote, stay for at least 30-45 min. Other coyotes will often return to the site, sometimes very quickly.
Their eye sight and sense of smell are way better than you think. They usually see, hear, or smell you long before you've ever seen them.
Practice long range shooting abilities, wind reading, judging animal distances traveled in your scope for follow up shots and double/triple kills. Shoot a light recoiling rifle, practice racking another round immediately after the shot and staying in your scope the entire time. Don't zoom in too far, use the scope FOV to your advantage. Lots of times dogs you never saw will run from behind cover after killing one. Use a suppressor as often as possible.
If you're truly in it for depredation and/or wanting furs or bounties, trapping supplemented with good rifle hunting strategies works well.
