I'll keep this short and brief so i'll summarise how Nines met up with UMP45. As always, if you dont wanna be spoiled, dont bloody hover, you will only have yourself to blame for spoiling yourself.
Prior to 404 being made, Nines was originally a civilian A-Doll tied to a criminal organisation involved with doll trafficking, despising every minute of being with the company, Reina wanted out asap, while wandering about and pondering ideas she bumped into UMP45, seeing her as a potentially high selling doll, she tries to "kidnap" her... but fails and gets beat up by her instead.
After the initial failed attempt, Reina went back to wandering around and stumbles across her again and again, and gave herself an idea, which involved using UMP45's hacking capabilities to sever her ties with the organisation while nabbing their banking information and freeing any locked up dolls in the process, This lead to Reina bringing UMP45 into a secluded location where they could hack into the companies security network, however UMP45 tripped up a node and activated the security systems which Reina ejected herself out asap, because she got what she came for leaving UMP45 locked in the system, although she was about to leave, Reina started feeling guilty and was worried about her being locked in, she didn't think she was gonna be locked in for so long, so she tries reconnecting herself only to see nothing in the network, empty a complete void, shortly afterwards Reina was knocked out.
A while later in a hidden location around the city, UMP45 confronted Reina and had her tied up and told her that she destroyed the network and asked why Reina left like she did. The two argued over a few things before parting ways, however Reina felt unsatisfied and wanted to repay her. Later that night the organisation started tailing UMP45 for destroying their systems, after a long pursuit Reina comes back but is entirely armed calling herself UMP9 and addressing UMP45 as 45-sis (Yon-go nee~), after battling it out with the organisation and fleeing from them, UMP45 questions how she was able to refit herself, Nines responded by saying she had connections (Dier) and that if UMP45 had nowhere to go, she could join her and hunker down with her friend and take on jobs for him. Promising reasonable pay and UMP45's freedom as well, she was still too cautious and was unsure if she could trust Nines, which Nines... promptly cut her eye to prove her loyalty... on the wrong eye though, which she noticed afterwards, after the 2 reached an agreement UMP45 started addressing UMP9 as "Nines".
After the upgrade, Nines wakes up in Diers workshop at his mansion and the whole process is complete with Nines ending off by saying to herself: "That’s right... What I’ve always wanted is to help 45-nee fulfil her wish. I’ll do it, and then hear her tell me everything about her past from her own lips. Ah, I’m looking forward to that day."