Cats are not the easiest to train to walk on a leash, at least not like a dog. You can always try a short leash and just let him drag it around in the house. Lots of treats helps too, if he's got a favourite. A light cat leash is the best to use. When I used to take my cats out on a leash and harness, it was more a case of just following them around while they explored. My one cat though once he figured out it was time to go in the house would lay down and refuse to move. I'd have to pick him up and take him back in, with him snarling and growling the whole time.
There is a drawback to taking them out on a leash, once they discover how much fun it is out there, they become escape artists! Wouldn't be so bad in an apartment, I would guess.