I have had the site online for 6 months now, and I recently updated my Meta Description on a website page. The search engines still display my old description for that page, How can I update my site in the search engines so my new meta descriptions are displayed. I think that, that would make be a good video
Essentially its a will be updated as soon as Google comes back to your website again. If your website isn't changed that often, it can take some time.
Even on my site it takes 2 – 3 days for new content or changed content to be indexed by Google.
You can try using a ping service or share your website on some social media profiles to try and get the Google bots attention.