hurts less than getting eaten by a coyote

Walking your cat is a great way to get them outside, but (depending on the individual) it's quite different from walking a dog. Most cats aren't very interested in the actual walking part of walks, and may be much happier finding a nice bush to sit under for half an hour. However a leash is a great way to keep your cat supervised and under control for outside visits, either in the back yard, around the block, or to a nearby park.

Other warnings: starting them young is ideal, but older cats can get used to the leash with a lot of patience (on both of your parts). Cats that were previously outdoor cats will have the most trouble adjusting to their loss of freedom, but indoor-only cats may be excited for the opportunity (or terrified: pushing your cat a little out of their comfort zone is okay but don't overdo it!). A well-fitting harness/vest is crucial, and even then a very determined (or scared) cat can probably wriggle out so be prepared. Keep a very close eye on your cat's emotional state and be ready to go home at signs of anxiety. Low-stress outdoor places (with few cars, dogs, screaming kids, etc, and with some form of cover like trees and bushes) are best especially to start. Treats and verbal encouragement, paired with small steps and lots of patience, are key! Above all stay consistent: once you've made the decision to make your cat leash-only, don't let them go outside without it: your cat needs to make the connection that they have to be on a leash if they want to enjoy the outside.

My neighborhood has had at least two flier campaigns in the past year for cats who slipped their leads and disappeared. Best of luck for those who find it novel but I'm gonna keep it simple and just keep the cat inside.