I have a credit union and that seems to be one of the best ways, low rates, lets you use for dealer or private party, finance up to 100% value of car, longer terms, etc

I only want a loan for a few thousand and will be paying about 75% of the car with cash.

Do I just walk into my credit union, they run a credit report and I tell them the car I am looking at and they hand me a check and make me sign a bunch of paperwork? Somehow I have a feeling it's much more involved?
Do they have to inspect the car (what if the car is far away? Do I go drive the car, decide I want it then go get the loan and then come back?)

Never done this, so TIA