Your local animal shelter needs people to foster kittens. Ideally the pregnant mother will give birth to kittens in your home. You'll keep the kittens until they're either a certain age (like 10 weeks) or a certain weight (2 lbs). Then they go back to the shelter to be spayed or neutered, given their vaccinations, then made available for adoption.
Typically the shelter will provide all the supplies you need for the cats. Including litter box, litter, scoop, beds, food, etc.
The second picture is a very sweet, very cuddly 6 month old kitten who's FIV+. That's like HIV in cats. He's in a home with another FIV+ kitten. They need a permanent home with no other cats or with other FIV+ cats. FIV can cause a lot of health problems or they can enjoy good health for a long time. Typically there aren't enough fosters even for healthy cats. Finding fosters for special needs cats is even harder.
Your shelter also needs people to foster dogs. Some are terrified there. Others grew up undisciplined and need a lot of work to make them adoptable.
My wife and I have fostered about 25 cats over the last 4 years. We currently have an 18 year old cat that was considered unadoptable because of her health. We'll have had her for a year by next Friday. She's doing fine. We also have one that wasn't eating at Petsmart. She stays in an extra bedroom and we visit her there. She's young and front declawed. We expect her to be adopted at any time.
And of course, one of the hazards of fostering is that you keep one from time to time. Myu wasn't eating well at Petsmart and she was scared there so we took her in. She's tiny, very sweet, and cuddly. When new people come over she'll just jump in their laps.