When was the last time you saw a cat on a leash? If your response is what I expect it to be, that's reasonable since most cats reject this kind of "therapy."
This is why the first and most important element is patience. It goes without saying that the cat will not accept such a proposal without some kind of disagreement. Anyway, if we're talking about an apartment cat, we can argue that it has to grow accustomed to the notion that it's not a given that anything terrible will happen once it's out of the home.
Create a surrounding area for your cat using your imagination initially. And don't forget that the cat would want to climb anything. Your cat may be drawn to high plants or low trees.
Purchase a collar for the cat and work on getting her accustomed to it. It is critical that it be worn just around the home at first. The leash must be handled in the same manner. Encourage her after a few days by going small distances on the leash and enticing her with a toy or some food. Then go for brief walks outside the home. One day at a time, increase your distance. Choose calm areas and make sure she is used to the outside city sounds.
If you truly want to teach her to walk on a leash, take her with you when you go shopping or on longer outings.
You can eventually get her to accept routes with heavy traffic, but it is critical that she feels secure and understands that she can depend on you. If she wants to rush about, make sure the collar isn't too tight.
You may even put a bell on her collar to help you locate her if she runs away or hides behind a bush. It will prevent her from hunting, but look on the bright side. You can track down your cat even if she goes away or escapes from the collar.