The following are important indicators of a happy, healthy bird:
The bird should be active, alert and interested in its environment.
Make sure feathering is shiny and without bare patches.
The eyes should be bright and clear with no discharge or swelling.
Nostrils should be clear of any blockages and a uniform size and shape. A flush of red can indicates an infection of the sinus cavities, whereas a scaly appearance around nostrils indicates scaly face (common in Budgies), a disease caused by mites.
Upper and lower parts of the beak (the mandibles) should meet cleanly, with no signs of separation.
Feet should have all toes, although a missing toe or claw for a pet isn't a bad thing, but more than one toe or claw gone will hamper the bird's perching ability. The bird should be able to grip its perch or your hand firmly. The feet of a young bird should be smooth and soft. Older birds have feet which are more scaly. Excessive scaliness is not good, and can be indicative of vitamin A deficiency.
Breathing should be regular and even. No wheezing, snorting or straining allowed.
The bird should not be too skinny - it should be well fleshed out.
Turn it over and check the vent area. It should be clean and clear of stains or dampness.