Google JSON API is the foundation of SearchMash, an experimental site created by Google.
So how do you get the search results using this API? You just load this page:
http://www.searchmash.com/results/[query]. You just have to replace [query] with the actual query. If you use this format: http://www.searchmash.com/results/[query]?i=11&n=10, you request 10 search results, starting with the result number 11. The formats for image search, blog search and video search are:
The JSON object you get from Google has a list of members that are very easy to understand, like: estimatedCount (the number of search results) or results, which is an array that describes the search results. To make cross-domain requests, you may need to create a web proxy, like shown here.