How do I repair or replace a broken cast iron toilet flange?

You need a toilet repair ring. Goes on top of the broken one.

https://www.homedepot.com/p/Oatey-Oatey-Stainless-Steel-Replacement-Flange-Ring-427782/303864005

https://www.homedepot.com/p/Oatey-1-4-in-PVC-Flange-Spacer-435192/303864021?MERCH=REC-_-PIPHorizontal2_rr-_-303864005-_-303864021-_-N

I won't need a spacer as the flange is already above the tile level.

I purchased a repair ring. However, I don't see any way to anchor it on top of the existing flange.

I found several videos on YouTube I hope this one helps...

https://youtu.be/uRGr_y4eqV4

Sounds like it is time to replace the old cast iron altogether with pvc. Hard to say without a photo, but it is tough working with cast iron, and trying to make a mend.

Here's a pic to show what I'm dealing with. That's just cardboard on the left side.

They make plenty of inserts to replace the ring. They have a flange that slips down into the pipe Oatey ABS Twist-n-Set Open Flange is sold by Home Depot but there are several styles. It's an easy fix.

Does that mean I need to remove the old broken one first?