I have two cats which I've trained from an early age to wear a harness and walk leashed. They do great.
Here's what I did:
I put the harnesses on them and gave them treats for getting through the process for about week or so to associate that wearing leashes is a positive thing. I didn't take them out on walks or anything, I just did it to get them used to it. They didn't seem bothered by wearing a harness. Now they come running when I get the harnesses out and sit there patienty while I suit'em up.
Next, I let them outside under my close supervision. They had to wear their harnesses to go outside. I also bought some 4mm climbing cordellette (you could use anything but I went with 4mm cordellete because its lightweight but not too thin - like parachute cord - to be uncomfortable for me to hold onto) and made a leash with a small screw-locking carabiner that I bought at REI (though you could buy them at a hardware store) which I clip to their harness loops. Then I just let them run around free but with a leash dragging behind them to get used to being outside like that. When I let them out now (since I live just north of downtown Denver in a busy inner city area) I keep them tethered to a tent stake in the yard with about 15 feet of parachute cord. They don't seem to mind. They do like being off leash better, but they take what they can get. When I move to Montana and live in a rural area, they'll get to roam free.
Next I held the leash and followed them around the yard. I didn't force them to follow me as they will resist if pulled. Instead let them lead the way around the yard and just follow behind to get them used to that.
Taking them out of the yard is tough. Don't pick times of the day which are busy, like when people are getting home from work, etc. Cats like early mornings and twilight and feel more comfortable at those times of day being outside. Let them lead the way and just follow behind them. Don't expect to do some serious mileage or even go a few feet beyond the fence at first. I also would carry them a ways and then let them go back to the yard while I followed behind. Eventually, as they got comfortable, they started to walk further and further.
Remember cats aren't dogs and won't just go go go. They like to stop and smell everything, rub against fence posts, roll around on the cement or on dirt, get easily spooked, trot along at a pace slower than yours, etc. And if they get tired or hot, they won't move. And remember to be generous with the treats.
I've taken my cats hiking (and its easier off leash) in the Rockies and they LOVE it - they've even climbed an 11,000 foot peak. They follow slowly and still investigate everything, but if I get 20 feet away they stop doing whatever it is they're doing and will rush up to follow me. By doing this they've gotten better at being walked on leashes. I've taken them on an overnight backpacking trip as well and they hiked they whole way to the lake (it was only a mile and a half). Dogs off leash is the biggest hazard so I try to be aware of other people and animals around my cats so I can quickly pick them up and move away from the other people or dogs. Other than that my cats are totally extreme, er whatever, dude.
I'm currently training them to ride on my shoulders and backpack. Its tough but treats really work. Chloe, who is really furry, will be my skiin' cat - not down hill, just touring.
