Like most learning, this is easiest if taught early in life so the cat grows up comfortable with a leash and harness. The training technique is the same for young or old, it is just slower in a cat over 6 months old.

Note that not all cats will accept a leash and harness. Since cats are not pack animals, it is not natural to travel with others.  So, allow plenty of time and give plenty of praise.

Introduce The Harness
Obtain a quality harness and fit it comfortably to the cat. When you first introduce the leash and harness, just leave it near the cat's food bowl, bed or favorite sleeping spot.     

You will need to decide if you want the cat to wear the harness all the time indoors, or only for walks. If you intend to leave it on all the time, put it on and leave it on, so the cat becomes accustomed to it as soon as possible.

If you plan to take the harness on and off, the best time to introduce the harness is just before feeding time. Let the cat wear it during the meal, then take it off afterwards. The idea is to get the cat to associate the harness coming on with something good happening. Taking it off is probably a reward for the cat.

Begin Leash Training Indoors
Once your cat is comfortable wearing the harness, attach the leash and let the cat drag it around the house for a few minutes. Gradually increase the amount of drag time. During this period, give lots of attention and cat treats. Try to make the harness and leash a good thing.

Praise constantly at first while the cat is walking on the leash.

The first time you hold one end of the leash should be during feeding time. Have the cat's food bowl in one hand, and the leash in the other.  Walk around the house calling the cat to follow you for a few minutes. If the cat balks or stops, don't pull on the leash. Just wait, and encourage the cat to come to you and the food. If the balk continues, drop the leash and walk to where you normally feed the cat and put down the food. Let the cat drag the leash more before you take it up again.

Outdoor Walks
The first thing is to make sure the cat is well identified with a tag and possibly a chip. Bring food treats and start when the cat is hungry. Go for a short time, and basically follow the cat while you hold the leash. Use the food treats, and back away if the cat comes. Give treats for coming toward you while you are holding the leash. Also try putting a food treat several feet in front of the cat. Then, hold on to the leash as the cat goes for the food. Praise constantly at first while the cat is walking on the leash. Consider using a retractable leash to avoid tangling.

If the cat stops to sniff, or just balks, remain calm.  Don't pull the leash. Instead, ignore the cat and only give attention and praise when he or she is walking on the leash. Gradually increase the time spent walking on the leash. Hopefully, the cat will come to understand that the leash is the ticket to exploring outdoors so the harness and leash will become good things.

Parasite Exposure
By taking the cat outdoors, you may be risking exposure to fleas. For this reason, you will want to consult with your veterinarian regarding effective flea control, and be sure your pet is up to date on all vaccinations.