Before you put a harness on your cat make sure it's a cat harness not a dog harness and that you've got the right size for your cat.
How do I choose the right harness for my cat?
Wearing a harness is not a natural experience for a cat. In fact, wearing anything around their body is not natural.
Most cats will simply flop on their side if you just straight-away put a harness on them when they've never worn one before. Having something wrapped around their chest triggers the instinct to go limp when a predator has them in its mouth.
Although it can be funny to watch, just know that you may be creating a negative association for your cat with the harness. What that might mean is even more time getting your cat used to wearing a harness because now you may have to overcome a negative association that you just introduced.
It may seem counter-intuitive but you may be able to save yourself some time by introducing the harness more slowly instead of all-at-once. The keyword is patience.
Get your cat used to seeing and smelling the harness first. Leave it somewhere that your cat hangs out and will notice it (e.g., near where your cat sleeps or plays or eats or hangs out with you).
Once your cat is OK with that (no negative reaction to it) then you can get your cat used to how it sounds. Most cat harness have fasteners that click together or velcro (hook and loop) that rips apart. Some fasteners buckle like a belt and make no sound.
Expose your cat to that fastening sound in a way that's not scary while your cat is otherwise occupied (e.g., being pet, eating a treat, etc.). Be brief and see how your cat reacts. You may have to take a pause or provide reassurance before doing it again.
Remember what you're doing is getting your cat to the point where these things are accepted as no big deal while also avoiding any negative associations.
The next step is getting your cat used to the touch of the harness. You can do this in a playful or loving way by just rubbing the harness gently against your cat. Your cat may want to inspect the harness. If so, let your cat look at it and smell it. By rubbing the harness against your cat you're also giving the harness your cat's smell.
The last step is putting the harness on your cat. Before you do this make sure you understand how the cat harness should be worn. Some harnesses are placed over the head first, others can be stepped into as they're pulled over the legs, still others are layed on the back and fastened underneath.
How do I choose the right harness for my cat?
The harness doesn't need to be fastened at first if it's a harness that can lay on your cat without being fastened. You can just place it on your cat, provide reassuance, and eventually fasten it if your cat's OK with that or try again later. The harness also doesn't need to be adjusted to get a perfect fit yet.
The goal at this point is to have your cat wear the harness for brief periods of time to allow your cat to get used to having it put on, wearing it, and having it taken off.
It's possible your cat will still flop over with it on at first. If that happens try distracting your cat from the harness being worn by doing something else like playing with your cat, giving treats, loving on your cat, etc. If it's fastened than try leaving it unfastened for awhile if it's the type of harness you can do that with.
Once your cat is OK wearing the harness for extended periods go ahead and begin adjusting the harness for the best fit. The goal is not to restrict your cat's movement and have your cat be comfortable yet still keep your cat from wiggling out of the harness.
The harness shouldn't be too loose nor too tight. You should be able to easily slip one finger underneath the straps or material (two fingers if you have small hands or thin fingers). Make sure it's not so tight or high up around the neck that your cat has trouble swallowing or moving. Also, be sure the harness is centered with the leash attachment in the middle of the back.
Remember, the key is patience. Your cat will more or less let you how the process is going.