I want to give away some of my cats, but they are already settled in our house. How should one proceed with this?
Look into local rescue organizations or humane societies/no-kill shelters. These places will frequently be able to take over the work of rehoming the cats for you, and at a bare minimum will be able to provide you with resources to help you safely rehome them.
For the cat's welfare, it's important that the home where they're being placed be evaluated to some degree. With rescue organizations, this is often through a combination of an application, interviews with the potential adopter and one or more references, and sometimes a home visit or interview with the potential adopter's veterinarian. There is also a fee connected to the adoption, which both helps to fund further rescue work and helps to reduce the risk for the cat--if the adopter is willing to hand over $100-$200 to take the cat home, they're going to be far more likely to take care of that animal than someone who takes it for free. Additionally, a typical rescue contract will have clauses that the pet must be returned to that rescue (for safe rehoming) if the adopter can no longer care for it, and that if it is learned that the pet is being abused or neglected, the rescue has the legal right to seize the pet and return it to the rescue.
Animals that are given away as free often end up as "bait" animals (for dogfights), fed to other animals, used in laboratory testing, resold for a profit, abused, neglected, or may end up in a hoarding situation. There's no checks in place to ensure the person taking the animal will provide veterinary care, or hasn't been legally barred from pet ownership (which happens in cases of extreme animal cruelty or neglect).
I have had to rehome several cats/kittens through the years. By far the best method was to put a flyer in my office breakroom with pictures of the cats/kittens.
I created flyers for vet offices and the local feed store but those were not successful.
I had tiny success with a Petfinder type of website. I recently acquired a puppy through a Facebook group. So, the web definitely has options for you.
In the end, it has always been my office, and word of mouth among friends who assisted me the most in rehoming my cats and kittens.