There is no guaranteed fast way. But a link from a very respected website will help, for example if you could acquire a link from the Guardian or BBC website.
Add new content in your website, and build backlinks, plus wait. Hopefully, you will get out of sandbox.
Build more links using different anchor text - Keep on optimizing your site and adding fresh content. then ---> just wait
get a link from W3C or any other monster super site. like obama or Hilary website, never heard about sandbox
Do you know what's the cause of your sudden being sandboxed? If you didn't do anything wrong then you can write an email to google webmaster support with explanations of what happened to your site and asking for consideration to re-index your site.
Keep posting good quality content daily and try to get good links from High PR sites, Then google automatically remove your site from sandbox. once your site is out of sandbox, don't loos your consistency, try to post at-least 1 article daily.