First of all, get the right harness for your cat. Go to your nearest pet shop and you will find a decent selection of cat harnesses. Make sure that you purchase one that fits your cat comfortably and is not too tight. If you have any issues, get some help with the salesperson as they are in a good position to help you find the right harness for your cat.
Get your cat accustomed to the harness. It is a good idea to leave it around the areas where your cat likes to eat or sleep. This way, the cat will not freak out when you try to put the harness on it.
Once your cat has seen the harness around the house, it is now time to slowly put it on your pet. Make sure you put the harness on the cat very slowly. If the cat starts to get irritated or angry then leave it alone and try it some other time. If you do manage to get the harness on the cat then make sure it is kept very loose in the beginning. Take a few days for the cat to get accustomed to the harness and slowly start to tighten it a little. If your cat puts up a decent fight when you tighten the harness then remember to take it off immediately and try it again later.
After a few weeks your cat should get used to the harness. You can now attach a leash and try walking around the house. Your cat will start to learn different commands that you can use to get it to follow your lead.
When the indoor leash training is complete, you can easily move outdoors with your cat. Remember to take it slow in the beginning as your cat becomes accustomed to the harness and the overall feel.