How can I wire a new iMac to an old one to migrate data?

Information clipped from a web search.

How to connect two Macs to use Migration Assistant?

1.  Thunderbolt is the fastest method and is available on all Macs from 2011 and later. Expect to transfer at least 3 GB per minute. You’ll need a Thunderbolt cable.
2.  Ethernet is available on desktop Macs, Windows PCs, and older Mac laptops. Expect to transfer 2 GB per minute. A Thunderbolt to Ethernet adapter (or USB 3 to Gigabit adapter) adds a network port to Macs that don’t have one. You’ll also need an Ethernet cable.
3.  Firewire was common on older Macs (2008-2011). Use a Thunderbolt to Firewire adapter and Firewire cable for 2 GB per minute transfers. Stuck with an old Mac (2002-2008)? You might need a Firewire 800 to Firewire 400 6-pin cable for 1 GB per minute transfers. 
4.  Wi-fi is a last resort. You’ll want to put the computers as close as possible to the wi-fi hotspot and try to shut down any other computers that may compete for bandwidth. If both computers and wi-fi routers are 2013 or later (with 802.11ac), you can achieve almost 1 GB per minute. Older systems with 802.11n may take 3 minutes to transfer 1 GB.

Use Migration Assistant. Apple describes how to migrate your data using this application in this support document.