Any bird you bring home should be quarantined from other birds you own for a minimum of 30 days, and 45 is even better. Place it as far away from the others as possible and feed and care for it last, washing your hands before and after. Birds under stress (such as moving to a new home) are more susceptible to disease. If a bird is a "carrier" of a disease, stress is likely to cause symptoms to be exhibited. A settling in period will ease the stress of the new bird and give you the opportunity to observe his behavior and physical condition.
A new bird may not eat right away in his new home. A spray millet attached over his seed dish will usually help direct him to his food as well as entice him - few birds can resist millet sprays.
Do not leave birds out of their cages unsupervised. Too many accidents can happen.
Keep your birds' wings clipped. Too many birds have flown the coop, so to speak, even though "they never flew off before". All it takes is once. You probably will never see it again if it gets outside.
Unclipped birds can get a pretty strong flight up, even from room to room, and birds have died after slamming into walls, windows, and mirrors. Most birds will stay tamer if kept clipped, also.
The band on a bird's leg is either open (with a break in the metal) or closed (a continuous band). The band is used to identify the bird, however there is a slight possibility of it posing a threat. If something becomes tangled or caught in the band, the bird may "hang". Keep an eye on open bands to be sure they don't open further. If they do, they can usually be closed with finger pressure. That said, do not assume anything dire will happen if your bird is banded. I band all my babies, and the only band-related problem I've ever had was with finches. The wicker nests can sometimes get hooked onto a leg band. It's important to remember that overlong toenails will usually pose more of a problem in that respect, though.
Wash all fruits and vegetables (fresh) before serving as they have likely been treated or sprayed with pesticides or preservatives.
Many houseplants are poisonous. If you are not sure of the safety of a specific plant, keep the bird away from it. There are many places to find lists of safe plants, especially on the internet.
Flea sprays and powders are toxic to birds. If you use these products, be sure your bird does not come into contact with them. If you've treated your pets with flea products, wash your hands after petting your four-legged friends and before handling your bird. It's not a good idea to let your bird walk on Fido, no matter how cute it is.
Non-stick coating on cookware (Teflon, T-Fal, and others) release toxic fumes when overheated to temps beyond 500+ degrees. If you use these, as I do, never leave something unattended that might boil dry or burn. These fumes can kill your birds in a matter of seconds. The non-stick drip pans for use under stove burners should not be used at all.
Fumes from hair dye and aerosols can kill your bird. Remove birds from the area in which you need to use these products. Be sure to ventilate the area before returning the birds. Birds' respiratory systems are much more sensitive than ours, so use caution when using any spray, cleaning product, etc. That doesn't mean you can't use any aerosols, but USE COMMON SENSE AND CARE.
Cats and dogs, no matter how cute and cuddly, and no matter how they've never in the past even looked at a bird, CAN and DO kill birds every day. Take precautions!
Get as many good quality books on your type of bird as you can. Then read them! There are some good magazines out there, too. Bird Talk has many good articles that will help with your bird care. Yes, there will be some contradictions among the books and magazine articles. Not everyone agrees on the best way to take care of the birds, but the bits and pieces you pick up from every article you read will all add to your knowledge.
If your bird is tame, PLAY with it! It wil be a lot like having a feathered dog, and it will crave affection and attention. Do not shower it with limitless attention at first if you cannot realistically keep it up. Try to spend a certain amount of time wih your pet every day, at the same time if possible. That way it will become a habit for you and your bird, and you will both look forward to it.
Enjoy your bird for what it is. Not every bird can talk or sing opera, and not every bird will be devoted to you. If you don't have preconceived expectations you will not be disappointed and can enjoy your bird's personality, whatever it is.