How to leave the sandbox?
A site enters the sandbox, because it is penalized by Google, the crawlers of the search engine have calculated that the content on the site is intended to artificially obtain a good ranking in results.
The first thing to do to get out of the sandbox is to delete from the content all possible causes of penalties, then you must work to obtain quality backlinks.
A site may be penalized because of an sudden increase of links from a same site or lot of directories, because of hidden text in the content or other such artifices...
Whatever the site has moved to the sandbox because it has been restructured or because it has been penalized, the means to retrieve its ranking are the same: getting the trust of search engines by a minimum of popularity. Some ways to achieve this:
- Remove all the causes of possible penalties such as hidden text, a partial content duplicated over all pages, a massive link exchange ...
- Remove multiple redirects.
- Encourage links with a useful and original content, with a friendly look.
- Use a spell checker. I use that of LibreOffice.
- Publicize the site. Some well chosen directories with no backlinks required by them. Needless to include the site in quantities of directories with a low PageRank in internal pages.
- Make scoops. Publish your news in digg-likes or press release sites.
- Do not place reciprocal links to other sites nor use any such techniques prohibited by the webmaster guide from Google.
You will gradually leave the sandbox. Backlinks will appear gradually in reports on GWT, and the crawler will come more and more frequently.

Leaving the sandbox or Alexa mystery?
References
- Guidelines to webmasters. To do and to avoid according to Google.
- The PageRank and Sandbox patent gives some indications about sandbox causes.
- Google's algorithm. Explains how the score of a page is evaluated.