The first point to make is that it is not a good idea to think about “making” your cat happy. It implies that you are trying to force your cat to the happy. It is better if you make the environment in which she lives and your behaviour better which will lead to her happiness. Being happy is a natural consequence of circumstance and it cannot be forced.
I think that there are two central ways which will lead to your cat being happier. The first is to make the environment in which she lives as good as possible so that she can behave as naturally as possible within it. If she is able to express her natural behaviours it must help her to become happy. This is because the opposite is true. If an environment is unsuited to a domestic cat and if the behaviour of her partner is unhelpful then she is liable to be less than happy or even unhappy.
The second way which leads to cat happiness is to ensure that you create as close a bond between you and your cat as possible. If she is very close to you emotionally she will obtain emotional warmth from your presence. A consequence of emotional warmth is contentment. Once again the opposite is true. If a cat owner is difficult with their cat or even hostile towards them, it is impossible to envisage that the cat can be happy. She is liable to be anxious and anxiety is counter to happiness.
A lot has been said about creating an environment inside the home which suits a domestic cat. You will find answers on this all over the Internet. Jackson Galaxy, the well-known cat behaviourist, has a book on the subject and he describes the making of a cat environment “catification“. You probably know the answers but in brief it includes providing high places for a cat to rest and feel secure. This is because cats think vertically as well as horizontally. They are somewhat arboreal in their behaviour which means that they like to be in trees. Many small wild cat species like to spend a lot of their time in trees. The domestic cat has inherited this trait.
Other important aspects are a calm environment, a predictable environment, routines and rhythms of life which your cat has learned and which provide reassurances, few strangers or no strangers coming into the home, and outside area which might be enclosed so that she can smell the air and feel the grass under her feet, excellent food and places to hide when she feels the need to do this.
In multi-cat households it is harder but essentially you will have to make sure that each cat has their own litter box plus one extra and each cat has their own food bowl and water bowl. This avoids conflict. It avoids bullying. Ideally the best work is carried out before adoption in multi-cat households because you want to do your best to make sure that they get along. I don’t think you ever quite overcome cats being antagonistic towards each other in multi-cat households no matter what you do because it is about feline chemistry. Cats have friends like people. If they are unfriendly towards another cat it is hard to overcome that emotion. Don’t have too many cats. I think a maximum should be about two or three but this is a personal viewpoint.
However, the more cats you have the harder it is for contentment because, for one, you squeeze the amount of space they have from their lives and in a home they already have much less space than they would normally have if they were free-living. Although domestic cats are very adaptable.
But space is a factor, there is no way to avoid that. Some people ask if a cat can live happily in a one-bedroom apartment. Perhaps they can but it will be less likely than if they were living in a large house with an enclosure attached. And it will be harder again if there are other cats in the apartment who don’t get along. And harder still if the owner is away from home all day long at work.
There are many other things to think about which I think it will be better for you to read by clicking on this link which takes you to more articles on the topic.
I believe that domestic cats can become more anxious than people realise. If they bond well with their owner it eliminates this anxiety or reduces it tremendously. You bond with your cat by spending time with her, being gentle with her, respecting her as a cat but treating her as a member of the family, providing excellent food, allowing her to make choices, allowing her onto your lap when she wants to be there, allowing her to be on your bed at night if she wants to be there, keeping her litterbox clean, providing an outside enclosure if that is allowable and practical, building a window box if an enclosure is impossible, petting her gently and in a way that she likes and for a duration that suits her. You will learn what she likes through careful and constant observation. Stick to it. In short genuinely love your cat. That always makes them happy.
Flea comb her daily in a gentle way if it is possible. It is possible with shorthaired cats but far more difficult with long-haired cats. Keep her flea-free. Keep your home flea-free. Stick to rhythms and routines. Make sure your life is the same every day if you can so that she finds life predictable. Predictability promotes happiness in a cat because it reduces anxiety.
Once again, you can click this link to read some more articles on bonding with your cat and being friendly with your cat.
These are my ideas. They come from personal experience and knowledge. You may have more ideas. In the interests of cat welfare please share them in a comment even if you disagree but always be polite please.