How to move contacts from flip phone to iPhone?

I got so tired of my buggy Nokia 6350 that I went to my service provider's website (AT&T) and bought an iPhone 3GS. When it arrived I read the instructions carefully and started the upgrade/activation process. Everything went fine until near the end.

I got to the page where they ask you to take the iPhone apart and make sure the numbers on the inside match the ones they show as being the phone they sold you. Just before that step, but on the same page, is a comment about moving all your names/phone numbers off the old phone and onto the iPhone. The link took me to a page where I had to select the phone the numbers were coming from (my lousy Nokia 6350) and the phone the names and numbers are going into (the iPhone). That in turn generated a popup that showed a diagram of a cell phone that looked like my Nokia with instructions about taking my new SIM (presumably from the iPhone), inserting it into the Nokia, and following a few more steps to copy the names/numbers from the old phone to the SIM for the iPhone, The diagram and instructions were pretty minimal.

But I didn't do any of this because some questions came to mind. First of all, why were the instructions so vague, and more importantly, was the SIM from a smart phone really compatible with a little flip phone? I had to leave the next morning for a family event where I talked to my brother, who works at a tech support call center for a major phone company (not AT&T).

He told me there was a possibility that my Nokia would look at an unfamiliar type of SIM and just format it. Wipe everything off of it. He suggested I instead use my card reader to copy everything from the Nokia SIM into a folder on my PC, then get on a forum like this one and find out if in fact this flip phone-to-smart phone information transfer has any hazards? And how to handle them?