“Into the system?”, he repeats, not sure what the sentence means.

"Well, we have to get tax money from things like people building houses or offices or mines so people don't get to have parks or start their own mines anymore, and we think it's important that people always think in terms of money, so almost all that tax money goes directly just to people. And afterwards we talk about things like building subways and roads and playgrounds and all those kinds of things, using the money that we could otherwise get directly ourselves."

"I... don't understand", Kellen replies, more confused by this explanation than he already was before. "The system?"

"The money system! We have currency for emergencies, but the money system is much easier because you don't have to carry the money around, or worry about dropping it somewhere."

Kellen nods, “ohh, okay. Do we do it now? How do we do it?”

"Well, usually you get to be in it when you're born, and the parents use your money for you on your behalf. But if they missed you when you were born, or something went wrong, you go to a police station, register all the information in your eyes and fingers, and get a new account in the system, losing all the money in your old account if you had any money or an account."

That sounds surprisingly simple! Although he doesn’t know if he’ll get in trouble for not being registered before. Won’t the police expect him to have some sort of legal proof of his existence? Which doesn’t exist here, since he pretty much appeared out of thin air, so he won’t be on their database. Well, they’ll face that problem if it becomes one and try not to worry when it might not matter. 
“So… is a police station near?”

"Unfortunately not, it'd take a bit of a subway ride. But they can't really close, can they? So we can get over there and get you in today, it really doesn't take long."

“Okay”, he nods and covers a yawn. It isn’t all that late yet but he’s been up for a long while. Kellen still wants to go get registered into the system though, so he heads for the door.

Cynthia leads Kellen onto the subway, taking him all the way to the nearest police station. She's let them know the situation in advance, so the machine that takes the fingerprints and the eye scan should be ready. "This man hasn't been joined the system yet. He needs to be given an account." She motions for him to get his fingerprints taken and his eyes scanned, in front of the bored-looking police officer waiting behind a counter.

Things get done swiftly and Kellen is glad that he earlier thought about how to spell his name in the local writing system. It would have been embarrassing to get asked how it was written and have no answer! It still makes him feel awkward anyway when he gets asked questions and stumbles over the words but not as badly so. All in all, it goes pretty well and they can leave the station with an account for Kellen in not much time. 

Kellen receives a card with a special film that makes it impossible to see anything when not looking at it straight on. It has a the information needed for accessing his account. "Next, you'll want a phone to actually get to use it. But maybe we'd want to purchase that tomorrow?"

He puts the card away into his pocket after examining it a bit (the special film is pretty interesting). Kellen then yawns again before shrugging and replying to Cynthia, "You know best. I don't need it today, right?"

"No, there's really no rush!"

He smiles, "We go back to your house?"

"We do that, yes!"

And so they can both take the subway again, exit near her building, and walk the last short distance. 

Cynthia walks over to her sleeping bag, making herself cozy in it. She's thinking of reading a bit on her phone, before finally finding some sleep; she knows that it's going to feel amazing.

Kellen also lays down wherever Cynthia tells him he should sleep. He's looking forward to getting some rest, it's been a pretty intense day. He's arrived at a different world, crammed as much of its language as possible into his brain, visited a museum... and he's also used some magic. He's been intentionally not thinking about that. He'll have to see if in the morning he still feels a bit magically tired, at least to decide if he should avoid using it again here. 

Cynthia insists Kellen sleep on her bed; beds are comfortable for everyone, but a sleeping bag only really works for the person it's designed to fit.

The sleeping bags he knows don't work very well for anyone but he'll take her word for it. He's too sleepy to try to argue. Sleepy enough that he falls asleep almost as soon as his body touches the mattress. 

The next morning, Cynthia wakes up, sitting on her phone at the dining table and wearing just her special underwear designed to match her skin color as perfectly as possible.

Amongst the first things Kellen does after waking up is checking on his magic reserves. Fortunately, they feel pretty much full again, so he shouldn't need to worry about them unless he uses them up all at once. 
Soon after that he gets out of bed and he wasn't expecting to find Cynthia looking just about naked when he steps out of the room. So he freezes by the door and instinctively mutters an apology in his native language. 

Cynthia just smiles and waves at him. "You can come in if you like!" She stretches her arms a bit. "Clothes like these are pretty standard and part of most anyone's wardrobe."

Kellen waves back and nods, still slightly reluctant as he steps closer to the dining table and her. “Good morning.”