Dr. Foster and Dr. Smith of the Veterinary & Aquatic Services Department had an interesting entry about bird behavior. They have a detailed description about the things birds do and what it means.
Pepper, our pied cockatiel, and the Lovies are fond of beak grinding and hanging upside-down in their enclosures. This means that they are happy. They also have a habit of bobbing their heads when they see people. This means they are trying to catch attention.
Pepper has a habit of spreading his wings in a quasi-predatory pose, which can mean either one of two things: 1)he's stretching, or 2)he's showing off. He also has a habit of calling out to us when we're home, because he really doesn't stay in his enclosure that often. (He mostly stays there to sleep and eat. We also put him in when we open the windows, so as not to risk him flying out.) One annoying habit that Pepper has is that he tends to cry when we leave the room so we have to answer his call to reassure him that we are coming back.
Lovebirds and cockatiels are smart birds that require constant stimulation. If a bird starts feather-picking (this is very different from preening) and chewing on its feet, it could mean that it's either bored or upset about something. Spend a portion of the day with them. Make toys out of cardboard material, toothpicks popsicle sticks, raffia, etc. Put their enclosures where people normally hang out like the livingroom. Do not put them anywhere near the kitchen (especially when you're cooking) as certain chemicals found there can be toxic to birds.
To know more about pet behavior, read the article on Pet Education.