Trying to figure out how to connect Ethernet to my iMac

The new 24" iMac model does not have a built-in Ethernet port in its case. The Ethernet port is now built into the power brick of the upper tier models and must be configured for an extra $30 when purchasing a base model.

see "Connections and Expansion" at > iMac 24-inch - Technical Specifications - Apple

If purchased a base model 24" iMac that does not have an Ethernet port in the power brick?

Then you can get and use a > Thunderbolt to Gigabit Ethernet Adapter - Apple

Normally you use a short CAT5 Ethernet cable between the Mac and the modem or router.

What is it you can't do?

You can help us help you: Writing an effective Apple Support Commun… - Apple Community

Or buy a dock with an ethernet port, and several others besides.

Good point.