How do I program my iHome light plug now that the iHome app has been sun settled?

You can turn on/ off manually with the Home app which you should have from the beginning of setting up your light plug. Now to set programs you need to have an Apple TV or HomePod from there I’m trying to figure how it gets programmed

Well, it is what it is. iHome is shutting down their service. You can likely still control some aspects through Home if the bulbs are HomeKit certified. But, you're probably out of luck for other fancier features.

You likely will not be able to use any of the "fancy" features of the bulb unless you have the app. But, it should still work as a light bulb.