My new mac is telling me my old mac needs to be updated but my old mac is up to date. I'm trying to transfer my files to the new mac but from reading here I shouldn't be doing that wirelessly anyway. What is the simplest way to do this?

My new mac straight out of the box is telling me that my old mac {running OS Yosemite 10.10.4 early 2008 model} needs to be updated before continuing with file transfer. My old mac says he's up to date! I'm trying transfer files from the old to the new. From reading other posts I shouldn't be doing this wirelessly anyway. Can someone please give me very simple step by step instructions on how to best to transfer the files? A friend suggested a FireWire {?} cable but the computer shop people said that the two computers are too different to be able to do that. They mentioned ethernet cables but then lost me....... Any help would be greatly appreciated 🙂