Top tips
Never leave a cat unattended when using a harness.
When fitting the harness should be snug but not tight you should be able to get 1 finger between neck and collar and 1/2 fingers around girth strap
Know your environment be aware of poisonous plants or hidden dangers such as ponds or large trees to climb
Be aware of other animals that may cause problems such as loose dogs if you are walking in a public place having somewhere safe to pop your cat if their is a loose dog is a good idea such as a cat carrier/backpack
If using a retractable leash be aware of letting you cat get too far from you. The leash may also get tangled
Hot vehicles/pavements etc. just like dogs cats can burn their toe beans quite easily also avoid travelling in hot cars and never leave your cat unattended in a car.
All cats are individuals some love going out others will prefer the safety of indoors. Have patience and do not force them.
The first step is to get your cat used to the harness indoors. first just put it next to them, when they are comfortable with that place it on. most of the time they will either walk sideways or just flop on the floor, do this on and off for a few minutes each day until they are happy, using clicker/treat training is good for this step, also play with them.
Attach a leash and walk around indoors again until your cat is completely comfortable
Take them out in a quiet secure area let them lead you. Do not pull on the lead. Things can seem a little overwhelming at first, if they get scared bring them back in, try again another day.
When its time to come in call their name and once in reward either with a treat or play
Cats act completely differently to dogs, they will lead you and are very easily distracted, always be calm and be there to protect them.
Walk next to or just behind them never pull them along