Just looking for a plugin to make this process easier and noticed this thread. Awhile back, I integrated into a website that I operate on wordpress.
1. You first need to create a page on your worpdress installation that will host both the google search box and the search results code. You need to do this first so you can get the link that the search box will submit to.
2. On Google, in your customer search engine visit the “code” page and put the url for your wordpress page in the “Search box and search results code for your website” section.
3. Back on the edit screen for the page you created in wordpress, paste both the search box and the search results code for your Google cse into the page. Make sure you are on code view.
I hope this helps…now off to see if I can find an easy plugin for the same. Please post it if you find it.