Their API details can be found here
Custom Search JSON/Atom API | Custom Search | Google Developers[
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To pre-empt your next question, no there is no way of doing this for free. Google is a business, they make money by showing ads in their search results so if you use an api you skip that feature so they are going to charge you. There isn't any other way of getting the data that does not violate their terms and conditions. Google have worked for a decade to build their service and just because it is on the internet doesn't give you the right to use their hard work for free.