How long is a piece of string? In my experience Google is quick to crawl a website for the first time but slow to re-crawl it… at least a few months. It really depends on your website, including how often you regularly update with fresh, relevant content. Get onto the Google Search Console and use all the nifty tools there.
Try these links too…
https://support.google.com/webmasters/answer/6065812?hl=en
http://www.seoblog.com/2014/06/long-google-reindex-site/
http://stackoverflow.com/questions/9466360/how-to-request-google-to-re-crawl-my-website