检索 is more formal and often used with an abstract object such as information, or abstract information of some objects, such as books (you don't really 检索 the physical existence of the book, instead you 检索 the information of the book, like title, author etc). You can see it as a query.
找 is simply "to look for". And it's not very formal since modern Chinese prefers words with at least two characters unless it's proper noun, or in existing collocations.
Here are some examples:
You can 检索:
You can't 检索:
Unless you are trying to 检索 their information.
But colloquially you can 找 information.
So in summary:
You 检索 to 找 (look for) something by examine their information, e.g. the title of a book, the manufacture of a product, the subject of an article.
You 找 simple to look for or seek something. You can see 检索 as a subset of 找