How do I connect a 2017 MacBook Air and a 2012 iMac

Connect them for what purpose, exactly? For file transfer, connect them with a TB2 cable. Then use target disk mode. You can use the same physical setup to use Migration Assistant.

network the 2 macs

you can drag files and other fun stuff

The problem is the iMac won't start, but it will boot in target mode, and I need some files off it.