A thorough patent search will involve both keyword and classification searching and will cover both US and international patents. It will likely take a significant amount of time to conduct these iterative searches, so you will want to keep track of your searches (and relevant patents, as you find them).
It is also a good idea to go back to the 'Patents' tab in this Guide and look at related guides, or contact the relevant subject librarian, for guidance on other literature sources related to your invention/idea.