Taking your cats for walks on a leash
Despite the independent nature of the cat, many cat guardians have successfully taught their kitties to walk outdoors. While it is a natural thing to take a dog for a walk, it really can become a natural thing for a cat as well.
Training your cat to the leash is best done in small steps. First, allow the cat to get familiar with the leash by placing somewhere it can be sniffed and evaluated. Then, in baby steps, put the leash or walking jacket on your cat.
Your cat may get scared the first few times venturing outside. This does not mean that your cat can not learn to walk on a harness. Be patient, and make the outside encounters as quiet and interesting as you can. Keep them short as well. A short fun time outside will make a good impression on your cat.
All the new sights, sounds, and smells are bound to be quite overwhelming to your cat, and this is where your immense patience has to come in.
Don't buy a leash that is designed for a small dog, but instead look into purchasing a leash or lead that is specifically designed with a cat in mind. These leads wrap around your cat, giving you control of the cat and keeping the cat from choking itself in a frantic attempt to get away.
Once kitty has gotten used to, or somewhat used to, wearing the harness at home, you can try to ad the leash. At this point many cats will have malfunction of their legs... or won't be able to walk straight. Not to worry, for most kitties the excitement and stimulation of being outside make them forget that they are on a leash.
While persistence and patience pays off in making your cat get used to not only a leash and harness, but also going outside, if it is obvious that your cat is not getting less stressed and is indeed suffering, then maybe you are better off finding some other way for your cat to enjoy the outdoors.
Trying for some time in baby steps is the way to be successful, but there are cats who just won't have any part of this. Be observant. If your cat gets a little more comfortable each and every time, then continue taking her out. Short trips with lots of praise and treats.
You may find that eventually your cat actually enjoys the walks outside, and gets really excited over the prospect of heading outdoors. It's a great way to allow your cat to explore without worrying about where it will wind up.