Okay, I got this to work again. I'll write the author shortly.
In the meantime, if you'd like to use this, do as the author says here:
As there's no longer an iframe option, though, choose "results only" for the layout. I chose "minimalist" for the style, but it probably doesn't matter. Click "save and get code".
Once you've enabled the plugin in your WordPress installation, paste that code into the second box on the config page (the search results one).
So, that takes care of how to display the search results. But you'll need a search box too. For that, I found this page on Google's site:
I used that code, but had to get rid of the last line - it was showing the "Google custom search" image below the search box, not inside. As the page says, find and fill in your search engine ID. Paste the code into the first box of the WordPress plugin config page, and you're done! Save and go to your site to test.