I have been searching around the docs but can't seem to find information on how to setup some sort of workflow so that when an editor chooses "Send to Publish" the correct editor(s) get notified that there is content ready for review. Does anyone know where in the docs it talks about setting this up?

You’ll need to hook into a notification from the sounds of it, here are the docs: https://docs.umbraco.com/umbraco-cms/reference/notifications

If I am reading that right this means to do something as simple as notify an editor when something is ready to publish I have to hand code a special notification service? That seems really odd that something so basic, and what I would expect to be default abilities for a CMS, has to be coded by hand.

Have you tried Umbraco Workflow? It's a commercial product, but does have a generous free tier.

I can't aford things and really all I want is some method to alert the right user group/member when an editor has something ready to publish. This, to me, seems like a very basic and normal function of a CMS so to not have that built in seems like a huge oversite.

The user who wants to be notified needs to open the action menu on the highest up node they want notifications on and go to notifications tick the options they want emails about

What your describing (and a lot more) is very free in Umbraco workflow though. And a much better experience then the notification system (for which we expect no more new features to be built).

Is there somewhere in the docs that talks about this? If I do a seawrch for "workflow" I just get results for forms, custom notifications and some document type things that are not relavent

It's an add-on package: https://umbraco.com/products/add-ons/workflow/

Thanks. I will take a look at that.