Once one understands why your pet Kakariki behaves as he does and how you may be able to help or adjust that behaviour you can begin the training process. My way has always been to start with the bird in a cage or small flight and slowly present my hand to the bird, depending how each bird acts determines how fast or slow the process goes, some are quite good and accept my hand close if it is not touching them, almost immediately others freak out and are off before I get the chance to move so much as my arm. Every step should be specific to each bird, as each bird will react differently. This is true to most species of bird too in general Kak’s are quite easy to tame compared to say a Grey. Once some trust has been established I start with a small piece of millet spray that I can hold out to them, this then in time is left in my hand for them to come on to, use of the words step up can be used here if you so wish, If biting occurs you must try to ignore this as pulling away establishes dominancy in their favour. All this is determined by the speed the bird wishes to go at, not any speed that I set. This is soon replaced with a sunflower, meal worm, piece of fruit or the likes. I will often touch their feet or belly with my fingers from my hand when they are sitting there, and start to fetch my other hand in for touching too. Soon your Kakariki will have a good trust of you and the next stage begins.   
Now this is where it all differs from most other birds, Kakariki are fiercely independent so once they’re out that cage or small confinement flight and because of their love of flight it can seem like it has all been wasted, this is true to hand reared Kakariki to, once flight is gained and independence achieved they are off. This is the hard part as an owner as you have spent all that time taming and now they don’t want to know you, but you’re missing the main point here, they are now somewhat humanised and the biggest hurdle of trust has been established and they are now behaving as a Kak does and no amount of taming will change that. It’s now time to encourage them to you from a distance (not a confined space), again food is the best way, they are very curious birds one could even say jealous of food possessions that you may have this is their nemesis it may take time and remember they won’t stay long, but they will come eventually. Remember don’t use this method to catch your bird to put them away in their cage or you could lose all your work as they will soon learn that food and you mean being put away.  This method has worked for me many times, occasionally like with Ruby at present regaining that contact can take time. I also think that other birds being around while sometimes can be of benefit, as they can see your interaction with them can also be a disadvantage as jealousy can enter the fray from your established birds.       
Again this is my experience my view others might do it different most find food in one way or another beneficial Good Luck