Hopefully, you have received a healthy young cockatiel. It can take changes in temperature, but not rapid changes or cold drafts. The best way to monitor health is through fecal output. Your new “baby” may have diarrhea for 24 hours after taking him home - this is due to the stress of the change and is not abnormal. After that, become familiar with what his healthy "poop" looks like and the quantity produced. Use paper in the cage tray and notice the fecal output - quantity and appearance - each day when you change it. If the quantity decreases or the appearance changes, look for other possible signs of illness. These are: perching on two feet instead of one when resting, "puffed up" appearance, discharge from nose or eyes, etc. Call the person from whom you received the bird if you see any signs of illness, or you can call an avian vet. First aid is always to make the cage warmer. You can do this by draping a towel over the top, sides and back (or wrapping the cage partially in clear plastic) and putting a heating pad under the cage. (There is an exception to the additional heat first aid step: if the bird has a head injury, do not give additional heat.)
In a perfect world, your baby was weaned onto pellets, fresh and frozen veggies, and a good quality vitaminized seed mixture. A mixture of cooked rice & wheat, plus thawed frozen mixed vegetables, broccoli, yellow or green squash and sometimes shredded apple (cockatiels don’t usually like fruits) make up a good fresh food diet, but your bird should also receive pellets and some seed (maybe 2 tablespoons a day). Most young birds also like Cheerios very much, as well as brown bread. If you want to cut back on seed consumption, limit the seed gradually. The best way to do this is to give pellets and fresh foods during the day and put a small amount (no more than 1/4 cup) seed into the cage about 7:00 p.m. at night, removing the seed bowl the next morning when you add the new fresh foods. After the bird is accustomed to this regimen, you can go to seed only every other day, etc. Don’t try to change your bird’s diet during the first month, though.
Cockatiels also like people food and a little won’t hurt - only one French fry per week, for example. Most birds go crazy for pizza. Don’t give your baby any chocolate, drinks containing caffeine, etc, though. Most natural foods are good for your birds, but avocado is an exception - it is toxic. Do not give your bird avocado.
Pellets and LeFeber's Nutri-Berries are a complete diet with vitamins and minerals in each bite. Fresh fruits and vegetables also contain some vitamins. Seed does not contain the proper balance of vitamins and minerals. If your bird eats seed, give it vitamins on its soft food twice a week. Keep a cuttlebone or calcium block in the cage, also. The bird may not touch it for months, but if it needs calcium, it will eat the cuttlebone. Cuttlebone does not spoil. If your bird receives seed as part of its diet, make sure it eats all the seed you offer. You can accomplish this by blowing off the chaff and putting the seed that was left back into the cage until all of it is gone. Seed is not bad for your bird and there are plenty of vitamin and mineral balanced seed diets, but it is only balanced if the bird eats all the seed and pellets in the mix. It is not a balanced diet if the bird is given the opportunity to eat only the seed it likes best and then gets a new supply the next day to do the same!
Give your cockatiel a bath tub or spray it with a fine mist, whichever it prefers, at least twice a week. I recommend keeping the wings clipped. Cockatiels fly high and fast and, if your bird gets spooked and flies off your shoulder, your chances of getting it back are small. If you use a concrete perch, as I do recommend, you will probably never need to have beak or toenails trimmed. Make sure the concrete perch is the highest one in the cage.
BEWARE! Fumes from Teflon cookware are toxic to birds. Supposedly, this is only overheated teflon, but there have been some reports of bird deaths when the pans didn’t seem to overheat. I recommend not using it at all. If you must use these pans (and this means all non-stick coatings), watch the pans carefully, use a fan, and have windows open. Aerosol sprays are also harmful as is smoke. In certain circumstances, both these can be fatal. It is better to have the bird in another room if grilling food inside (with heavy smoke production) or using aerosol products.
The above information is only a sketchy outline of what you need to do to keep your sweet cockatiel baby healthy. Join ACS, join your local bird club, read everything you have access to and then make up your own mind about the “details” of caring for your beautiful little companion.