Lot's of youtube stuff and info on the net. Just search "how to make a snare trap" or similar wording. You'll find out how to make snares for everything from rabbit and squirrel to coyote.
BUT, if you're wanting to make coyote snares exclusively, the suggestion in the previous post is spot on! Buy em cheap then you have all the parts AND good examples! All the parts except for the wire are reusable... you can get spools of wire cheap enough to make up new snares with the old parts to replace the ones that got all twisted and kinked up when you have a catch.