First, thank you for picking the baby up and wanting to take care of it. After years spent rescuing these guys, it amazes me how few people care or are willing to put in the effort. I’m also amazed by the wonderful people that do too. The advice to go to the vet was absolutely correct and I’m glad you’ve made an appointment.
Remember, kittens need to be kept warm. They cannot regulate their own body temperature and can become chilled very easily. They also become dehydrated quickly and require frequent, small feedings. Follow the instructions on the formula closely. Kittens under 1 week need to be fed every 2-3 hours; 2 weeks old need to be fed every 4-6 hours; 3 weeks old and above about every 6-8 hours.
Positioning is important when feeding kittens. Have it rest on its stomach on a towel/cloth so it has something to cling to and hold the bottle at a 45 degree angle, keeping a slight pull on the bottle. If it doesn’t suck on (or take) the nipple, rub its head or along its back. This will mimic the mother cat cleaning it and may stimulate it to want to eat. If you are using an eye dropper, be very careful not to accidentally force feed it. The kitten has to take the formula at it’s own pace. Kittens can, and do, aspirate the fluid into their lungs. This can be very serious, resulting in pneumonia and death. If it starts to choke, hold it upside down until it stops. Usually (but not always) you’ll know when the kitten is done eating when little bubbles form around it’s mouth.
When done, kittens should be burped just like a human baby but VERY gently. As someone mentioned, they also cannot control their bowels or bladder. You will need to moisten a cotton ball, tissue, or cloth with warm water. Rub its belly, genitals, and rectum gently to stimulate it to go. They’ll almost always urinate but defecate once or twice/day. A tip - count to 60 so you know you’ve given it enough time to go so you don’t stop too soon.
How can you tell how old the kitten is? Roughly:
The eyes open in 7-10 days
Kittens crawl around 3 weeks of age
The ears stand up around 3 1/2 weeks of age
Kittens start to play with each other and teeth start to develop around 4 weeks
Eyes remain blue until around 6-7 weeks (final color takes a few months to develop)
Most kittens start the weaning process around 4-5 weeks of age. You can tell if it’s time if the kitten is biting the nipple hard and licks formula from your finger.
If you have other pets, keep the kitten separate. Go so far as to wear different clothing/shoes when working with it so as to minimize transmitting anything. Keep its bedding very clean to reduce the risk of infections; use a lot of hand sanitizer (on yourself); sterilize the nipples/eye dropper before each use; and enjoy your new friend. It sounds like a lot of work (it is) but it’s great.
Good luck.