For finger training, there's a few very important things. You need to not react with any sound other than a calm, no bite when bitten. This takes practice. Then you need to not jerk away, take the bite so she learns your finger will not leave and she must get used too it. Talk gently to her the entire time you work on finger training. It takes time and practice on both parties, also try to remember, a beak is another hand for a bird, not every time her beak touches you is meant as a bite. She'll explore things by mouthing it.
For getting her used to fingers as a good thing, point your finger, thumb and the rest curled. Make sure she is looking at your hand. Now slowly move it towards her. When she nips or bites, curl the finger slowly away, no bite. Do not move the hand. When she calms down, uncurl and make sure she is watching, move your finger closer to her beak. When she is gently mouthing and exploring your finger, even grooming your nail for you, you will be ready for the next step. Remember to do it slowly though and talk calmly. If you make a big fuss over being bitten, some birds love the sounds you make and the reaction a bite can cause. It's almost like when a kid can make a parent break down and have a tantrum, the kid finds this hilarious because a grwonup is acting like a kid.
Next step is, see if a cupped hand, or a single, slightly bent finger is less scary. Where the finger game, you are aiming for having your finger near her beak, you want the cupped hand/bent finger over her head. When she freaks out and bites or nips, stop. Leave the hand where it is and say no bite. When she is looking at you, move a little closer. You want to go over the head and touch the back of the head/neck area. Right now,lightly. Gently stroke the feathers up, not down. This is grooming and she'll slowly learn that your finger or fingers touching her is nice. Again, if you are bitten, stay calm, do not move away and wait until she calms down. When she is enjoying your stroking, push your fingers lightly under the feathers to touch skin as you rub the feathers upwards. They love it when they realize you're grooming them, when you really dig in! But...you know, not hard to hurt them. Take baby steps It will take time for you both to learn. Eventually, she will have fun grooming you and may let you move to stroking or grooming more than just her head.
My Poopie, a tiel, loves to groom me when I allow him anywhere. Even my gums, I make sure I've brushed my teeth recently before I let that cute little head in my mouth, but he is gentle and will insist on grooming my entire head. He even grooms my ears and attempts to get in my nostrils. He does get mad and nip when I shoo him away. Once in a blue moon, the old fellow will lift a wing and ask me to rub beneath it, but this on his part shows a whole lot of trust. Mostly he's more a, I'll groom myself on you, groom you, let you rub my little head off and leave tiny poops all over you kind of guy. He's in his twenties and he literally begs me to rub his head as he turns it from side to side. I've timed it and he will have me rub until my finger is sore, two hours once and he still wanted more! I was worried about rubbing his feathers clean off and my finger was tired. But now I usually only do it for thirty minutes straight, tops. He's a spoiled oldster and knows it.
I'm special in his eyes, I'm the only one he lets touch under his wings and the only one he wants to rub his beak, under his chin, his neck and cheeks. Everyone else must rub the back of his head or get a good bite. He's a little cage aggressive, but I may have to change cages on him to fix that. He bites others, but nips and yells at me as he steps up. I attribute some of it to him being old and old guys are allowed to be cranky.
I'm looking forward to hearing more about your new girl and I'd love to help when I can. I love seeing people learn with their birds the do's and don'ts of handling. I feel it helps you strengthen your bond as you grow and learn to trust one another, together.
Also, touch training works wonders. You do need to have a stand alone perch, a thin dowel ( about finger width ) and whatever treats she adores, this will take some doing to find out! If she is cage aggressive, teach her to step up on the dowel. You can use this in the cage to bring her out. Do not chase her with it. This is also why a lot of people get bit, they try to chase their bird around with their finger and corner it. When there's nowhere to run, they get scared and bite. Don't stick all of it in the cage, have it about thigh high and ask her to step up. If she moves away, be patient or come back later.
Target training, you work on with the step up from the perch. Like the finger game earlier, you want to move the dowel to her face, but sideways this time. When she bites it, say a no bite. Stay still and go a little closer when she is calm. When she touches it with her beack, say touch. Praise and treat her. Eventually she'll learn touch means to touch the object in front of her face with her beak. Two days with the dowel, then two days using your finger. Then the same concept with the step up. Do not panic or scold if she is gently using her beak, some birds like to use their beak to help them step up. It's like a third hand/foot. Like and elephant's trunk. Use the dowel first two days, then your finger the next two. Training for touch and step up work best with clipped wings and on a stand alone perch because they do not have the option of flying to escape you and not learn. But you don't want to scare her either. You can try it without clipping, clipping is a little stressful on a bird. This is why you want someone else to be the bad guy and clip, so you are seen as the hero as you rescue, cuddle and love on them that the scary thing had happened. Each bird is different and the feathers grow back around three to six months and they can fly again. By that time, working with her, you can teach her a lot. It's a matter of treating at the right time, learning what scares her and how to tell before she feels she has to bite and waiting for her to calm down before moving further.
Hopefully I've helped some and not just talked your ear off. I look forward to hearing about your progress.