The short version
Budgies can learn to speak, but most people give up before the birds ever make a sound. The difference between failure and success usually comes down to patience and timing, not some secret training method. You need to pick the right words, repeat them at the right moment, and wait. A lot. The basic mechanism is simple conditioning through repetition. You say a short phrase clearly, and you say it repeatedly while the budgie is alert and paying attention. Most budgies learn two to five words over several months. A few learn phrases or short sentences. The bird's natural instinct is to mimic sounds it hears frequently, especially if those sounds are associated with social interaction. That's all the mechanism is. The execution is what people mess up. I started this process with a budgie I bought from a pet shop at three months old. She wasn't shy, but she also wasn't particularly social. Within a week she had started whistling the tone of my voice when I talked to her. That's the first sign you're on the right track. By week six she could say "hey bud" back at me. It took eight months total for her to learn about a dozen words, and some of those were only partially correct. She pronounced "computer" as something closer to "kum-pa-ter." She never said "hello" clearly. She just couldn't or wouldn't, and I stopped pushing it after four months of trying.
Here's what actually works. Pick one short word or phrase to start. Two syllables is ideal. "Hey bud," "pretty bird," "good boy," "come here." Something you already say naturally. Don't overthink it. Sit near the cage when the bird is awake and active, usually mid-morning is best. Say the word slowly and clearly two or three times. Then stop. Don't keep going. You're establishing the sound, not performing for an audience. Do this once or twice a day. Five minutes max. Consistency matters more than duration. The hardest part is knowing when to introduce a new word. Wait until the bird consistently responds to the current word. That means approaching the cage, making eye contact, maybe even making that familiar sound back. If you add a second word too soon, the bird usually just learns neither properly. I had another budgie, male this time, who learned "who's a pretty boy" as a single unintelligible noise. He'd try to say it but couldn't separate the phrases. I broke it down, taught "pretty boy" first, then later added "who's a" and he managed to put them together. That took about ten weeks total. There's a common misconception that budgies learn better from videos or audio recordings. This is mostly false. Budgies respond to social interaction, not passive listening. A recording doesn't look at the bird, doesn't react to the bird, and doesn't reinforce the behavior. If anything, recordings help slightly by providing more repeated exposure, but they won't produce a talking budgie on their own. The bird needs a real person making the sound. I tested this myself with two different budgies over a couple of years. One had a tablet playing bird speech recordings for hours daily. Barely any progress. The other had five minutes of my direct voice each morning. Learned about fifteen words. The difference is night and day.
Another thing people get wrong is training timing. Training right after feeding often backfires. The bird is too focused on food. Training right before bed tends to work better because the bird is calm and settled, but not so tired that it's sleeping. Mid-morning or early afternoon when they're naturally vocal is the sweet spot. If your budgie is screaming at the top of its lungs at 6 AM, that's not training time. That's the bird asserting itself, and reinforcing it by talking back just teaches it that screaming gets a response. Sometimes a budgie simply will not learn to talk. It happens. Females especially tend to be less vocal overall, though that's not a hard rule. Some males just don't have the inclination. A stressed bird, a recently moved bird, or a bird that's still settling into its environment won't learn. If your budgie hasn't made any vocal progress after three months of consistent effort, you might just accept that this particular bird isn't going to talk. That's fine. Most budgies don't learn to talk, and that doesn't mean anything is wrong with them. They're still perfectly normal birds. Positive reinforcement works if you use it sparingly. A tiny treat, like a small piece of millet spray, given immediately after the bird makes any attempt at the target word can help. But don't overdo it. You want the bird learning the sound, not learning that saying things gets food. The connection needs to be between the sound and social attention, not the sound and a snack. Overfeeding treats during training sessions can make the bird food-motivated rather than communication-motivated, and that changes the whole dynamic.
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If you want the best chance at success, start with a young budgie under six months old. They're more impressionable and their vocal apparatus is still developing. An adult budgie can absolutely learn to talk, but it takes longer and fewer birds succeed. I've had one older budgie, about two years old, who picked up "hello there" within a few weeks. He was the exception, not the rule. Don't expect quick results with an adult bird. The end result is usually a budgie that can say a handful of words clearly, maybe a few phrases partially. They rarely achieve perfect pronunciation. Their vocal anatomy isn't built for human speech. What you're getting is an approximation, and most budgies sound like they're mumbling through a mouthful of feathers. It's charming, but don't expect clarity beyond a few words. The whole process requires real patience, and you have to be okay with the bird setting its own pace.
