Coyotes can be caught and held with traps from 1.65/1.75 up to #3's comfortably. Sometimes there are trap restrictions based on state's laws... and sometimes by ethics... meaning if there is a small chance of catching a dog, then a smaller trap, like the 1.75 or #2 should be used because it's easier on the paw.
Make sure all your traps have a minimum of 2 swivels; 3 are even better. One at the stake end, one at the trap end and one in the middle. Swivels help keep the chain from binding and it's easier on the paw of your catch when the trap can spin freely.
Baits too have restrictions by state. There are a variety of coyote baits on the market. If you want to get your own, then rabbit, muskrat and beaver are good ones to try. Even horse meat will work well.... deer meat too. Don't use too much, just a chunk the size of a walnut will do fine.
Set your traps "upwind" of where you expect them to travel so they can smell the bait/lure as they walk by if they don't see your setup first.
As for as "look like", google "dirt hole" or "flat set" and that should help. It'd be nice if some of the members had a pic or two to share as a pic IS worth many words.
Wherever you see tracks or scat are good places to set traps. Along meadows, field edges, grass lines and trails are ideal too. The intersection of roads work good as well.
As for bobcat...
1 1/2 coils to #3's work good. Longspring traps work good too, but I prefer coils because they're more compact and easier to conceal and less work to bed.
For bait, muskrat and beaver work good. Hanging bits of rabbit fur or a feather or two on a string really draws them in visually. I like to hang a feather on a light thread about 3' off the ground with a swivel in the middle. The slightest of breezes gives good movement to the feather bringing them in for a closer look. Place it right behind the set trap. Placing a trap in front of a cubby set is a good set to use.
Bobcats like higher elevated areas if they are there. They like the edges and thick areas where game is at. One thing about bobcats are that they are a creature of incredible predictability at times. Once you spot a 'cat track, most often they'll be by within 2 weeks and almost in the SAME tracks as before. I've snared several bobcats over the years and it's fun!
Hope that helps some.
Take care,
iSnipe