Travis CI is a hosted continuous integration service for the open source community.
Essentially you set up a git post-commit hook that causes your tests to get run on every commit, against a number of different Perl versions, with databases and other services available if needed. And it's all free!
If you visit https://travis-ci.org/ you can get a feel for the interface and the tests that are being run. For a particular commit you get a build, for example WebService::Nestoria::Search build 1, which has a sub-build per Perl version, for example WebService::Nestoria::Search build 1.1 (perl 5.16). As you can see you get the full output from the Ubuntu VM that's running your tests, so if anything does go wrong it's pretty simple to debug.
For the rest of this post I'm going to describe the integration process, in particular hitting on how to make it work with Dist::Zilla-based projects.