What do I need to connect external hardware to new MAC?

See the following for an Apple adapter: USB-C to USB Adapter - Apple

There are also 3rd party adapters.

511pstl wrote:

I have a usb connected external disc drive but my new MAC only has the smaller c and thunderbolt ports.

What is the exact make/model of your external drive?

In general terms, if it's a USB drive you would only need a good quality USB cable with a USB-C plug on the end plugged into your Mac. There are also inexpensive adapters like this one to convert the rectangular USB-A plug on an existing cable to USB-C.

Or docks that have several types of ports.