All I want to do is a simple Google Images search. We were doing the old, really, incredibly simple way using the now completely deprecated JSON Image Search API.
That page now says it is included in Google Custom Search. The problem is that I don't want to search my own website, I want to search the web for images still. I cannot, for the life of me, find what the new way to do this is.
I have tried the Google API for PHP, it also works only with Custom Search which is only for searches on my website and not the entire web.
I have tried it using https://www.googleapis.com/customsearch/v1?key=MYKEY&cx=MYCX&q=candy and it's still searching our website only not the web in general.
Can someone point me to a documentation page that describes how to use an API to do an image search on the web in general and get results in the JSON?
You can indeed use the Google API for PHP. You just need to configure your custom search engine to search the entire web. To do this, login to your CSE settings at https://cse.google.com/cse/, and remove all sites. Then, change 'Sites to search' to 'Search the entire web but emphasize included sites'. Since you don't have any sites specified, it will just search the whole web.
You can test using the box on the right.
As for documentation, the CSE API is documented here https://developers.google.com/custom-search/json-api/v1/reference/cse/list#parameters