Normally, parakeets purchased when they are about six weeks old are either already tamed or easily tamed. Older birds take more time. The best time to finger tame your bird is in the early evening after it has eaten and when is less lively. The room should be quiet and free from distractions, such as TV or other people moving around. Open the cage door and slowly move your index finger toward the bird, whi will usually flutter away. Leave your hand in the cage for a few moments and then withdraw it.
Repeat this a number of times and usually by then, the bird will not flutter away. Next, slowly move your finger to your pet's lower abdomen and it will hop onto your finger. Do not try to bring it out of the cage at this time.
Once this has been done many times, over a few days, you can the slowly bring your hand toward the cage door -on which is a tidbit, such as millet spray- and chancer are the parakeet will hop onto the platform and peck at the spay. It may well also fly off the room. Do not chase it, but the patient and encourage it onto your finger again.
Always remember that a parrot will never step downward, only up, so the finger must be always higher than its feet. How quickly a budgie can be tamed it depends on the nature of the bird and the ability of its trainer to gain its confidence. A soft voice and slow movements are crucial. Never try to hurry things alone.
I recomends to only talk to your bird before starting the training lessos, so it will get used to you and your voice, talk softly and gently to him. Also, its better if you have it's wings clipped, it doesn't hurt them, and the feather will grow back in about 6 months, this will keep him from flying around, and you'll have more control over him.
Parakeets can mimic sounds if trained properly, you'll have to have a lot of patience and will to teach them.
Firstly, as with taming, ensure there are no distractions, including mirrors. Start with a single word, such as "hello", and repeat this many times. Never try to teach short sentences at first but concentrate on that first word until the parakeet learns it, otherwise you'll be doomed to failure. Once one word is gasped then a second can be tacked, then a third one and so on.
Once a parakeet developed his ability to talk it will learn many words not directly taught to it - which is why the more famous African Grey and Amazon Parrots include undesirable words within their vocabulary!
When one has a pair of birds then it is a cage of taking one bird to a separate room for its speech lessons. Why it is far more difficult to teach paired birds to talk it is much harder to overcome their natural desire to use their own language as it were.
Often, owners give up on their birds thinking they will not learn when it is really the fact that the teacher doesn't have the patience to persevere.
There are cds which can teach the bird to talk, they can be purchased on your local pet store.
Loui didn't learn to talk yet, but I'm teaching him every day. It is recommended to have 15-20 session per day. Talk to your birds smoothly and slowly so he understands the sound of the word, and repeat the word over and over again.
At the beginning they won't say the word clear, and they will mutter a lot, thats because they are figuring out the sound, but once they get they first word, they'll learn the next ones more easily!
So good luck with your training and I hope it goes great!