My budgie Smol won't shut up! It's true that some just aren't interested in talking and some love it, but I think it really boils down to having a really good emotional bond with your budgie. The more it likes you, the more it will want to mimic you!
Smol responds best to repetition (obviously) and very excited higher pitched voices. Also starting with something small I think is a good idea, maybe one or two syllables. Then giving them a bit of a challenge later on. Smol didn't start mimicking until I had him around 2 or 3 months. He now will pick up anything that fancies him if it's said only a few times around him! (I have to watch what I say around him honestly)
Another thing with getting them to say specific things is little reminders now and again. Over time Smol will forget a phrase or just lose interest in it, and I'll give him a little recap and repeat some phrases to him, he picks them up again really quick!
Again it really depends on the budgie, but either way communication with your bird is vital to your relationship with it! All birds love sounds, so talking to it is the best way to get THEM talking. Good luck!