You will need a call of some kind, whether an electronic call or handheld mouth call. A rabbit squaller or wounded rabbit from the electronic caller is my #1 used call. Don't be scared to get loud and rowdy with it. Handhelds are the cheapest until you figure out if you like coyote hunting or not. I have used a few electronic callers and they all work, but I believe in buying American, so I bought a Foxpro. After using it, they make the best e-caller, IMO. They make one now that is right around $169 and has 200 sounds on it. They also make one that is super simple and has 20 sounds on it for $109 but for an extra $60, why not get the better call with more sounds? You won't use all the sounds to hunt with, but they sure are fun when friends are over.
I have an electric decoy that spins a fake fur tail round and round, but you can get by with a feather hanging by a string on a stick, blowing in the wind. This is used to keep their attention off of you.
I prefer the wind to come from behind me and either blow at an angle to the left or right. If you know where they usually come from, you can use this to your advantage. If you don't know where they come from, study the area and set up with the wind at your back and hope they play the game.
Ex.- You are hunting your pasture looking North and the coyotes come from the right(East). The wind is blowing WNW, coming from behind you. Put your caller and decoy, if you have one, on the down wind side of you. The coyotes will try and circle to the down wind side and smell what is making the noise and inspect the decoy. This usually allows you to see them and before they can catch your wind and shoot them. If you have the wind in your face, they can and will circle behind you and smell you and you will never know they were there.
Learn how to lip squeak or use the back of your hand. This can get them to come that extra little bit you need for the kill or get them to stop for the shot.
I have better luck when it is cold, overcast and sprinkling/snowing than I do on cold, sunny bluebird days. If there is snow on the ground, it should up your odds too, because they will be hunting looking for warmth and energy.
You can learn a few things about howling at some point. It works pretty well during their rut, which is Jan-February here in Tennessee. I don't just sit and hunt with howls going. I tend to howl a few times in the AM at my first set and then use rabbit the rest of the day, with a few howls in the PM right before it gets dark.
Be prepared to shoot! Don't sit down and turn the caller on before you are completely set up. I have had coyotes come running out of the brush with less than a minute on the call timer.
I will update as I remember things or chime in if someone remembers for me....