Help Me Understand Next Steps On Buying This Used Car! [EASY Question] [Newbie Confused On Process]

Hey everyone. This is my first time buying a car and I'm wholly confused on my next steps. It's highly likely that I'm overthinking this and I just need some clarification. Here's a punch list of the timeline thus far:

-Did a ton of research and found a great car at a very small dealership

-Dealership is lightly sketchy but car is great, salesman gives me verbal agreement on price

-Got pre-approved for a loan with a credit union based on car year/mileage and verbally-agreed-upon price

-Called salesman at dealership to confirm pre-approval, salesman tells me I don't need to do anything else other than to come in to sign paperwork and pick it up

Getting confused on when in the process of when I actually pay for this thing.

I'm guessing the dealership will contact my credit union and cover it from there, right?