Before starting training with your budgie make sure you let your bird adjust to their new environnement. Baby budgie ( they have stripes all over their head) are easier to train although using the proper training an adult budgie is not impossible to tame. There are 2 methods most commonly used.* Also before taming I highly recommend you clip your budgie's wings for their own safety.
The first is the method where you slowly gain your budgie's trust.
Sit close to your new bird's cage each day slowly move closer. Only go as close as your bird feels comfortable. After she's used to having you near put your hand in the cage. Your bird will probably be frightened but just keep talking softly. Keep your hand in for a minute.Then the next day 2 minutes. Then 3 minutes. After that 5 minute periods are perfect. Soon your bird will become curious and step on your hande. Try to keep as still as possible. After 5 days of your bird perching on your hand try to move your hand back and forth slowly. She'll probably jump off but get back on. After she become comfortable with you moving your hand try to take her out of the cage. If she flutters to the ( which is really probable) Let her walk around for a couple minutes and then offer your perch as a finger. If she doesn't step up put slight pressure on your bird's lower belly. If that doesn't work cup your hads together and let her settle back on your finger. After 5-10 minutes (less time is your bird panics)Taking her back to the cage she should ideally ride on your finger and you can gently deposit back into her cage.
The second method is called heart which I used to train my budgie Elliott.
First you have to set up a small bird-proofed area ( which means no dangers that can harm your bird, like mirrors uncovered, open toilets, or a window which a bird can fly into in panic and break their neck, etc.)I used my bathroom. Get your bird's cage put it on the floor with a pillow (for your comfort). Now you have to get your bird out of the cage...2 things are going to happen you're going to get bitten and not complain about it!!!Don't wear gloves because your bird can become frightened of them. Using this method on my budgie I would suggest you take bandaids and cover up the fleshy middle parts of your fingers. Now open your cage door, secure it with something so that the door doesn't shut suddenly injuring your budgie. Grab your bird gently firmly but gently and fold his wings so that he can't flap and injure himself. Then place the cage out of your birds sight so now they have to depend on you for security. Place your frightened bird against your chest so they can hear your heartbeat and feel warmth. Their bites will probably diminish. As the regain compusure shift so that you use your index finger to stroke his back. When the feel more relaxed your ready for the next step, placing them on your finger. Your bird will probably flutter to the floor. Now just play with your bird in the confined area, using one hand to steer him to other. As soon as he jumps on a hand to avoid the other hold still. The whole taming session should take 15 mins or so. Repeat the process the second day. The third day instead of herding your bird with your hands offer a finger and say 'step up'. The next few days continue and try to move your finger with your budgie on it. Congrats! your bird is becoming your buddy!
**I got this Information from the book 'The complete Idiot's Guide to Bird Care & Training' by Jackie O'Neal This is the best book I've ever read on bird care and I suggest you run out and buy your own copy!!!***