I had SharePoint foundation and I need to use the NewsFeed.
So how can I make the web part available outside of MySites?
I think in order to use the social feature you need the SharePoint Server 2013.
Because their is no UPA/Mysite in SPF so you cannt use it as far i know.
If you are using the team site then Site feed feature will available. Check the feature comparison here: http://florianlaumer.wordpress.com/2013/01/15/sharepoint-2013-standard-vs-enterprise-vs-foundation-feature-comparison-matrix/
You can activate it by following these simple steps:
At the top of the site, click Settings > Site settings.
From the Site settings page find Site Actions then under it click Manage site features.
From the list of feature, find Site Feed then click the Activate button (if not yet activated).
Go back to your Site homepage and you should now see the Newsfeed link added from the left navigation panel. If you cannot see it, try to refresh the page. (Or Edit Page and add the webpart which is listed under Social Collaboration (Site Feeds))