You can train your cat to walk with a leash, but the first rule to this is Patience! Patience! and more Patience!
Cats need to be slowly coaxed into walking with a leash, but it can be done.
The first thing you need to do, is purchase a harness for your cat. One that fits her well, is no where near her neck, it should be a body harness especially designed for cats, do not use dog ones. You should also be able to fit two fingers under it. It should not be too tight.
Put this harness on your cat very loosely to begin with, and let her walk around the house, you can give her a little treat and distract her with lots of loving, if she is unsure about this thing wrapped around her. Some cats don't seem to care, others will take some extra time but will eventually walk with a leash.
After a couple of days of putting on and taking off the harness, it is time to move to the next step. Your cat needs to be happy and comfy at each step, if not, continue on that step until she is happy, it will not get better moving to the next step!
Now drop the leash on the floor near where she is playing, and near where she sleeps. Let her see it, smell it, she may even roll all over it and play with it, this is good, it will become "hers".
After a couple of days of that, now it is time to try attaching the leash to her harness and dropping it. she will walk with the leash on, but without you holding it. Let her get used to this for a day or so also.
Then pick up the leash and walk around the house with it, don't pull her around, let her get used to you being on the other end.
If all goes well at this point of walking on the leash, then you can venture outside. Start with your own backyard, and see how it goes. If she panics a bit, come back in the house, but more than likely, if you have been allow lots of time and patience to walk with a leash, you will be fine.
Take her out in the yard, and see how that goes for a few days, then venture out in the real world, and see how she reacts.
If your cat has never been outside, loud noises and cars may terrify her. My own cat is quite happy walking around the yard and the field behind, she hates the loud noises of cars. She is quite happy with nature and the sounds of trees and birds.
If you follow each step and take as long as it takes for your cat to get used to each stage, then you will eventually be able to have your cat walk with a leash, just like dogs do. This may seem funny at first, but it is no different than walking a dog, and much safer, especially if you live in town.
Another great option, if your cat absolutely hates to walk with a leash, it to create a home in the yard for her. You can get cat enclosures that are usually built with a window or door access.
I have seen ones that are built like a tent with a very tough screening fabric, and all kinds of climbing toys, and just the grass yard for the floor and enclosing a window that the owner leaves open in the nice weather so the cat can go in and out of the house, and be outside, but not in any danger.
There are choices now to keep your cat safe. Try to get your cat to walk on a leash, it is good for them to be able to do this. It will get them the exercise they probably need, and it is not bad for you either!
Promote play time with your indoor cat, to help keep their weight in check, as well as control when they eat. If you can afford one of these enclosures, you should look into them, they have become more and more popular, as many town are considering licensing and fining owners of roaming cats.