A new pair of lovebirds

Hello,

I am pretty new to training and taming parrots. I just got a pair of lovebirds, born in September, and I have no idea how to proceed on taming them.

Because of some issues, they got away right before putting them in their cage for the first time ever in their new home. I had to catch them and put them back in using a large towel, and then I let them sleep. They didn't move at all until the morning and little by little they found their way to their food ( they still haven't figured out where to drink) but they are rather terrified of me. I keep them 30 cm away from where I sit at my laptop and I talk to them pretty often. The male is pretty shy and inactive, he likes to sit around a lot, while the female is very curious and she was the first to map the cage and find the food.

How should I proceed to bond with them? I've read a lot of stuff so far, but I'd rather ask people here since it may be better. Please keep in mind that I have never tried taming birds in my life, but I am willing to learn and offer my lovely pair of lovebirds the best home I can. Thank you!

They are sometimes getting into small fights, nipping each others' beaks and they are absolutely terrified of hands. They aren't so afraid of me being close to them ( a few cm from their cage) but they go nuts if I raise my hand near them, even slowly. After just cleaning their cage they are mortified, sitting at the bottom of the cage.

I don't know what to do to get them used to me.